Title: Geometry Chapter 3
Course: quiz duplicate error

Q: Construct a line perpendicular to m through P. Then find the distance from P to m.

Line m contains points [Image] and [Image]. Point P has coordinates [Image].
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
A: [Image] [Image]

Write a two-column proof of the theorem.

If [Image], then [Image].
[Image]

Regina, age 10, is a fullback, or defender, for her soccer team. She kicked the ball from the corner of the sideline and the halfway line (denoted by the A below ) hard enough to go 120 ft. toward the forward (denoted by B) so the forward could take a shot on goal. Did her kick reach the forward? Explain and show your calculations to justify your answer.
[Image]