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 tojustify 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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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

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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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

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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