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1. Consider triangle AABC on the coordinate plane. Let P = (-2, 1) and Q = (2,1). Point P is on side AC and point Q is on side BC respectively. Vertex C is at C = (0,3). Vertices A and B are both on the x-axis. (a) Find the coordinates for A and B. (b) Find the midpoint of side AB. (c) What is the ratio of CP to CA? What is the ratio of CQ to CB?

1. Consider triangle AABC on the coordinate plane. Let P = (-2, 1) and Q = (2,1). Point P is on side AC and point Q is on side BC respectively. Vertex C is at C = (0,3). Vertices A and B are both on the x-axis. (a) Find the coordinates for A and B. (b) Find the midpoint of side AB. (c) What is the ratio of CP to CA? What is the ratio of CQ to CB?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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1. Consider triangle AABC on the coordinate plane. Let P = (-2,1) and Q = (2, 1). Point P is on side AC and point Q is on side BC respectively. Vertex C is at C = (0,3). Vertices A and B are both on the x-axis. (2,1). (a) Find the coordinates for A and B. (b) Find the midpoint of side AB. (c) What is the ratio of CP to CA? What is the ratio of CQ to CB? (d) What theorem justifies your result in part (c)? Hint: It is not similar trian- gles. (e) What shape is ABQP? You do not need to prove this result but you do need to justify it with reasoning. (f) The y-axis bisects angle BCA. Justify this result using the angle bisector theorem. (Hint: which ratios should you look at?)
Transcribed Image Text:1. Consider triangle AABC on the coordinate plane. Let P = (-2,1) and Q = (2, 1). Point P is on side AC and point Q is on side BC respectively. Vertex C is at C = (0,3). Vertices A and B are both on the x-axis. (2,1). (a) Find the coordinates for A and B. (b) Find the midpoint of side AB. (c) What is the ratio of CP to CA? What is the ratio of CQ to CB? (d) What theorem justifies your result in part (c)? Hint: It is not similar trian- gles. (e) What shape is ABQP? You do not need to prove this result but you do need to justify it with reasoning. (f) The y-axis bisects angle BCA. Justify this result using the angle bisector theorem. (Hint: which ratios should you look at?)
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