1.) in triangle tuv, y is the centroid. if yw=9, find ty and twa)ty=3, tw=12b)ty=6, tw=15c)ty=18, tw=27d)ty=27, tw=362.) in triangle tuv, y is the centroid. if vx=9, find vy and yx.a)vy=6, yx=3b)vy=5, yx=4c)vy=27, yx=18d)vy=13.5, yx=4.5

Part 1) Option C) TY=18, TW=27

Part 2) Option A) VY=6, YX=3

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

The centroid is located two thirds of the distance from any vertex of the triangle (the centroid divide the median in a ratio of 2:1)

Part 1) In triangle TUV, Y is the centroid. If YW=9, find TY and TW

step 1

Find TW

we know that

substitute the given value

Solve for TW

step 2

Find TY

we know that

substitute

therefore

Part 2)  In Triangle TUV, Y is the centroid. If VX=9, find VY and YX.

step 1

Find VY

we know that

substitute

step 2

Find YX

we know that

substitute

therefore