Answer:
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
[tex]YW=\frac{1}{3}TW[/tex]
substitute the given value
[tex]9=\frac{1}{3}TW[/tex]
Solve for TW
[tex]TW=9(3)=27\ units[/tex]
step 2
Find TY
we know that
[tex]TY=\frac{2}{3}TW[/tex]
substitute
[tex]TY=\frac{2}{3}(27)=18\ units[/tex]
therefore
[tex]TY=18,TW=27[/tex]
Part 2) In Triangle TUV, Y is the centroid. If VX=9, find VY and YX.
step 1
Find VY
we know that
[tex]VY=\frac{2}{3}VX[/tex]
substitute
[tex]VY=\frac{2}{3}(9)=6\ units[/tex]
step 2
Find YX
we know that
[tex]YX=\frac{1}{3}VX[/tex]
substitute
[tex]YX=\frac{1}{3}(9)=3\ units[/tex]
therefore
[tex]VY=6,YX=3[/tex]
