Question

How do I do this? Show all work please! THANKS

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Answer 1

the centroid in a triangle is the point where all the "medians" meet.

the medians are of course the segments going from a vertex to the middle of the opposite side.

now, one thing about the centroid, it cuts all medians in a 2:1 ratio.

by looking at the graph, we can see that BP is the longer, so BP : PM are on a 2:1 ratio, thus


`\bf \cfrac{BP}{PM}\implies \cfrac{7x+4}{2x+5}=\cfrac{2}{1}\implies 7x+4=4x+10 \\\\\\ 3x=6\implies x=\cfrac{6}{3}\implies x=2\qquad \qquad \qquad\qquad \boxed{PM=2(2)+5}`