To prove: Themedians intersect at P and P is two thirds of the distance from each vertex to the midpoint of the opposite side.
Answer to Problem 36PPS
The proof that the medians intersect at P and P is two thirds of the distance from each vertex to the midpoint of the opposite side.
Explanation of Solution
The slopes of
The slope of
The slope of
Now,
And,
Also,
Intersect AR and BS to determine the coordinates of P.
So,
The coordinate of P is
The measure of AP is calculated as,
The measure of AR is calculated as,
The measure of BS is calculated as,
The measure of BP is calculated as,
The measure of CQ is calculated as,
The measure of CP is calculated as,
Now,
And,
Also,
Hence, proved.
Chapter 5 Solutions
Geometry, Student Edition
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning