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Given triangle ABC has vertices A(-4,2), B(4,4), and C(2,-6), the midpoints of AB and BC are P and Q, respectively, and segment PQ is drawn. Prove by coordinate geometry that segment PQ is parallel to segment AC and that PQ = 1/2 AC.

Given triangle ABC has vertices A(-4,2), B(4,4), and C(2,-6), the midpoints of AB and BC are P and Q, respectively, and segment PQ is drawn. Prove by coordinate geometry that segment PQ is parallel to segment AC and that PQ = 1/2 AC.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter5: Similar Triangles
Section5.5: Special Right Triangles
Problem 37E
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Given triangle ABC has vertices A(-4,2), B(4,4), and C(2,-6), the midpoints of AB and BC are P and Q, respectively, and segment PQ is drawn. Prove by coordinate geometry that segment PQ is parallel to segment AC and that PQ = 1/2 AC. 

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