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, $3$:
$PS = 2$
