Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 5 - Relationships Within Triangles - Mid-Chapter Quiz - Page 316: 11

Answer

$CP = 4$ $PS = 2$

Work Step by Step

A centroid is the point where all the medians of a triangle meet. The median is said to be concurrent at point $P$. The centroid also divides the median into two parts where the one part coming from the vertex is two-thirds of the median and the other part attaching to the side opposite the vertex makes up one-third of the median. We can then say that $CP$ is two-thirds of $SC$ and $PS$ is one-third of $SC$. Let's set up an equation to find $CP$: $CP = \frac{2}{3}(SC)$ Let's plug in what we know: $CP = \frac{2}{3}(6)$ Multiply: $CP = \frac{12}{3}$ $CP = 4$ $PS = \frac{1}{3}(6)$ Multiply: $PS = \frac{6}{3}$ Divide the numerator and denominator by their greatest common factor, $3$: $PS = 2$
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