Title: Chapter 9
Course: quiz duplicate error

Q: Determine how many lines of symmetry each object has. Then determine whether each object has point symmetry.

[Image]
- 1; yes (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 2; yes (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 1; no (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 2; no (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
A: 1; no

Q: Determine how many lines of symmetry each object has. Then determine whether each object has point symmetry.

[Image]
- 6; no (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 6; yes (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 5; no (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
- 5; yes (A line of symmetry is the place where a figure can be folded so that the two halves match exactly. A point of symmetry is a common point of reflection for all points on a figure.)
A: 5; yes

Q: In each figure, [Image]. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.

[Image]
- Yes; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a translation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a rotation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
A: Yes; it is one reflection after another with respect to the two parallel lines.

Q: Graph the figure and its image under the given reflection.
[Image] with endpoints [Image] and [Image] reflected in the y-axis.
- [Image] (What occurs when the figure is reflected? How do the x and y values change?)
- [Image] (What occurs when the figure is reflected? How do the x and y values change?)
- [Image] (What occurs when the figure is reflected? How do the x and y values change?)
- [Image] (What occurs when the figure is reflected? How do the x and y values change?)
A: [Image]

Q: Name the image of S under a reflection in line m.
[Image]
- T (Find the line of reflection. Draw a segment perpendicular to line m from the given point. Locate the reflection point so that line m is the perpendicular bisector.)
- V (Find the line of reflection. Draw a segment perpendicular to line m from the given point. Locate the reflection point so that line m is the perpendicular bisector.)
- S (Find the line of reflection. Draw a segment perpendicular to line m from the given point. Locate the reflection point so that line m is the perpendicular bisector.)
- W (Find the line of reflection. Draw a segment perpendicular to line m from the given point. Locate the reflection point so that line m is the perpendicular bisector.)
A: W

Q: In each figure, [Image]. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.

[Image]
- Yes; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a translation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a rotation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
A: No; it is a reflection followed by a translation.

Q: Copy each figure. Use a composition of reflections to find the rotation image with respect to lines m and t.

[Image]
- [Image] (Reflect the figure over line m. Then reflect the figure over line t.)
- [Image] (Reflect the figure over line m. Then reflect the figure over line t.)
- [Image] (Reflect the figure over line m. Then reflect the figure over line t.)
- [Image] (Reflect the figure over line m. Then reflect the figure over line t.)
A: [Image]

Q: Copy parallelogram WXYZ.
[Image]

Rotate the parallelogram [Image]counterclockwise about point M.
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
A: [Image]

Q: Copy pentagon ABCDE.
[Image]

Rotate the pentagon [Image]clockwise about point Q.
- [Image] (First graph pentagon [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the pentagon rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph pentagon [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the pentagon rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph pentagon [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the pentagon rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph pentagon [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the pentagon rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
A: [Image]

Q: Copy parallelogram WXYZ.
[Image]

Rotate the parallelogram [Image]clockwise about point M.
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
- [Image] (First graph parallelogram WXYZ. Draw a segment from point M to point W. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points X, Y, and Z.)
A: [Image]

Q: Determine whether each regular polygon tessellates the plane. Explain.

equilateral triangle
- yes; measure of interior angle = 60 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 60 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- yes; measure of interior angle = 120 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 120 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
A: yes; measure of interior angle = 60

Q: Copy parallelogram ABCD.
[Image]

Rotate the parallelogram [Image] counterclockwise about point Q.
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C and D.)
A: [Image]

Q: Copy parallelogram ABCD.
[Image]

Rotate the parallelogram [Image]clockwise about point Q.
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
- [Image] (First graph [Image]. Draw a segment from point Q to point A. Use a protractor to measure the indicated angle. Is the parallelogram rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B, C, and D.)
A: [Image]

Q: Copy triangle ABC.
[Image]

Rotate the triangle [Image] counterclockwise about point D.
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
A: [Image]

Q: In each figure, [Image]. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.

[Image]
- Yes; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a translation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a rotation followed by a rotation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
A: No; it is a rotation followed by a rotation.

Q: Copy triangle ABC.
[Image]

Rotate the triangle [Image]clockwise about point D.
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
- [Image] (First graph [Image]. Draw a segment from point D to point A. Use a protractor to measure the indicated angle. Is the triangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points B and C.)
A: [Image]

Q: Graph each figure and its image under the given translation.

[Image] with endpoints [Image] and [Image] under the translation right three units and up two units
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
A: [Image]

Q: Copy rectangle JKLM.
[Image]

Rotate the rectangle [Image]counterclockwise about point T.
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
A: [Image]

Q: Determine whether each regular polygon tessellates the plane. Explain.

square
- yes; measure of interior angle = 90 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 90 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- yes; measure of interior angle = 45 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 45 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
A: yes; measure of interior angle = 90

Q: Determine whether each regular polygon tessellates the plane. Explain.

decagon
- yes; measure or interior angle = 144 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 144 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- yes; measure of interior angle = 36 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 36 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
A: no; measure of interior angle = 144

Q: Graph each figure and its image under the given translation.

[Image] with vertices [Image] under the translation left three units and down two units
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
A: [Image]

Q: Copy rectangle JKLM.
[Image]

Rotate the rectangle [Image]clockwise about point T.
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
- [Image] (First graph rectangle [Image]. Draw a segment from point T to point J. Use a protractor to measure the indicated angle. Is the rectangle rotated clockwise or counterclockwise? Draw [Image]. Use a compass to copy [Image] onto [Image]. Repeat with points K, L, and M.)
A: [Image]

Q: In each figure, [Image]. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.

[Image]
- Yes; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a translation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is a reflection followed by a rotation. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
- No; it is one reflection after another with respect to the two parallel lines. (Translations are compositions of two reflections. In order to be a translation, the two reflections must occur.)
A: No; it is a reflection followed by a rotation.

Q: Determine whether each regular polygon tessellates the plane. Explain.

octagon
- yes; measure or interior angle = 135 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 135 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- yes; measure of interior angle = 45 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 45 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
A: no; measure of interior angle = 135

Q: Graph each figure and its image under the given translation.

[Image] with endpoints [Image] and [Image] under the translation right two units and down three units
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
A: [Image]

Q: Graph each figure and its image under the given translation.

[Image] with endpoints [Image] and [Image] under the translation left two units and down one unit
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
A: [Image]

Q: Graph each figure and its image under the given translation.

[Image] with endpoints [Image] under the translation [Image]
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
- [Image] (Graph the original image. Determine how many units to add or subtract to each coordinate. Graph the new image.)
A: [Image]

Q: Use a matrix to find the coordinates of the vertices of the image of each figure under the given translation.

[Image] with [Image]; [Image]
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
A: [Image]

Q: Graph the image of each figure under a translation by the given vector.

pentagon [Image] with vertices [Image]; [Image]
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
A: [Image]

Q: Determine whether each pattern is a tessellation. If so, describe it as uniform, not uniform, regular, or semi-regular.

[Image]
- yes; uniform (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, semi-regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- no (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
A: yes; uniform

Q: Graph the image of each figure under a translation by the given vector.

parallelogram [Image] with vertices [Image]; [Image]
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
A: [Image]

Q: Determine whether each pattern is a tessellation. If so, describe it as uniform, not uniform, regular, or semi-regular.

[Image]
- yes; not uniform (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, semi-regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- no (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
A: yes; not uniform

Q: Determine whether each pattern is a tessellation. If so, describe it as uniform, not uniform, regular, or semi-regular.

[Image]
- yes; not uniform (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, semi-regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- no (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
A: no

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 3; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 3; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
A: [Image]; reduction

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 1; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 1; congruence (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 1; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 1; reflection (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
A: 1; congruence

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 2; enlargement
- 2; reduction
- [Image]; enlargement
- [Image]; reduction
A: [Image]; reduction

Q: What is the magnitude and direction of [Image]? Round to the nearest tenth.
- 11.2, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- [Image], [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- 10.3, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- 11.2, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
A: 11.2, [Image]

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 2; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 2; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
A: 2; enlargement

Q: Graph the image of each figure under a translation by the given vector.

[Image] with vertices [Image]; [Image], [Image]
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
A: [Image]

Q: Determine the scale factor for each dilation with center P.

[Image]
- –0.5 (To determine the scale factor divide the image length divided by the preimage length.)
- –2 (To determine the scale factor divide the image length divided by the preimage length.)
- 2 (To determine the scale factor divide the image length divided by the preimage length.)
- 0.5 (To determine the scale factor divide the image length divided by the preimage length.)
A: –0.5

Q: Determine whether each pattern is a tessellation. If so, describe it as uniform, not uniform, regular, or semi-regular.

[Image]
- yes; not uniform (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- yes; uniform, semi-regular (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
- no (Tessellations containing the same arrangement of shapes and angles at each vertex are called uniform. A regular tessellation is formed by only one type of regular polygon. A semi-regular tessellation is formed using two or more regular polygons.)
A: yes; uniform, regular

Q: Determine whether each regular polygon tessellates the plane. Explain.

hexagon
- yes; measure or interior angle = 120 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 120 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- yes; measure of interior angle = 60 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
- no; measure of interior angle = 60 (Determine the size of the interior angle of the regular polygon. If the size of the interior angle is a factor of 360, it can tessellate.)
A: yes; measure or interior angle = 120

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 3; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 3; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
A: 3; enlargement

Q: Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

[Image]
- 4; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- 4; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; enlargement (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
- [Image]; reduction (If [Image], the dilation is an enlargement. If [Image], the dilation is a reduction. If [Image], the dilation is a congruence transformation.)
A: 4; enlargement

Q: Find the magnitude and direction of [Image] for the given coordinates. Round to the nearest tenth.
[Image]
- 11.7, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- 3.6, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- 146.3, [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
- [Image], [Image] (To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.)
A: 3.6, [Image]

Q: Determine the scale factor for each dilation with center P.

[Image]
- –0.3 (To determine the scale factor divide the image length by the preimage length.)
- –3 (To determine the scale factor divide the image length by the preimage length.)
- 3 (To determine the scale factor divide the image length by the preimage length.)
- 0.3 (To determine the scale factor divide the image length by the preimage length.)
A: 3

Q: Graph the image of each figure under a translation by the given vector.

[Image] with vertices [Image]; [Image]
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
- [Image] (First graph the figure. Then, translate each vertex by the vector. Connect the vertices of the shape formed by the translation.)
A: [Image]

Use scalar multiplication to find the coordinates of the vertices of each figure for a dilation centered at the origin with the given scale factor.

Parallelogram RSTU with [Image]; 3

Graph each figure and its image under the given translation.

[Image] with vertices [Image], [Image], and [Image] under the translation [Image].

Q: Use a matrix to find the coordinates of the vertices of the image of each figure under the given translation.

[Image] with [Image]; x-axis
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
A: [Image]

Determine whether each regular polygon tessellates the plane. Explain.

Hexagon and equilateral triangle

Graph each figure and its image under the given translation.

[Image] with endpoints [Image], and [Image] under the translation [Image].

Graph the image of each figure under a translation by the given vector.

[Image]with vertices [Image]; [Image], [Image]

Graph the image of each figure under a translation by the given vector.

quadrilateral ABCD with vertices [Image]; [Image]

Omar is a professional gardener. He drew a map view of a garden on the following vertices: [Image], [Image], [Image], and [Image].
a.      On a coordinate plane, graph ABCD.
b.      Omar has a difficult time reading his graph. His assistant suggests that he should dilate the image with the origin as center and a scale factor of 4. Find the coordinates of the vertices of [Image].
c.      Graph and label the coordinates of the dilation [Image].

Copy each figure. Use a composition of reflections to find the rotation image with respect to lines m and t.

[Image]

Determine whether each regular polygon tessellates the plane. Explain.

Regular octagon and square

Determine whether each regular polygon tessellates the plane. Explain.

square and equilateral triangle

Allana drew the diagram below to show the front view of a teepee. Prove that [Image] is congruent to [Image].
[Image]

Determine whether each regular polygon tessellates the plane. Explain.

Hexagon and square

Q: Use a matrix to find the coordinates of the vertices of the image of each figure under the given translation.

[Image] with [Image]; y-axis
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
- [Image] (Write the vertex matrix for the given figure. Create a translation matrix. Add the vertex matrix and translation matrix together. The result is the vertex matrix of the translation.)
A: [Image]

Graph the image of each figure under a translation by the given vector.

rectangle WXYZ with vertices [Image];
[Image]; [Image]

Graph the image of each figure under a translation by the given vector.

pentagon [Image] with vertices [Image]; [Image]

Determine whether each regular polygon tessellates the plane. Explain.

19-gon

Graph the image of each figure under a translation by the given vector.

hexagon JKLMNO with vertices [Image];
[Image]

Use scalar multiplication to find the coordinates of the vertices of each figure for a dilation centered at the origin with the given scale factor.

[Image] with [Image]; [Image]

Use scalar multiplication to find the coordinates of the vertices of each figure for a dilation centered at the origin with the given scale factor.

Parallelogram JKLM with [Image]; [Image]

Use scalar multiplication to find the coordinates of the vertices of each figure for a dilation centered at the origin with the given scale factor.

Parallelogram ABCD with [Image]; [Image]

Graph each figure and its image under the given translation.

[Image] with endpoints [Image] under the translation [Image].