Question

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

A)Ty=3, TW=12

B)TY=6, TW=15

C)TY=18, TW=27

D)TY=27, TW=36

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

A)VY=6, YX=3

B)VY=5, YX=4

C)VY=27, YX=18

D)VY=13.5, YX=4.5

Answer 1

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

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

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

`YW=(1)/(3)TW`

substitute the given value

`9=(1)/(3)TW`

Solve for TW

`TW=9(3)=27\ units`

step 2

Find TY

we know that

`TY=(2)/(3)TW`

substitute

`TY=(2)/(3)(27)=18\ units`

therefore

`TY=18,TW=27`

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

step 1

Find VY

we know that

`VY=(2)/(3)VX`

substitute

`VY=(2)/(3)(9)=6\ units`

step 2

Find YX

we know that

`YX=(1)/(3)VX`

substitute

`YX=(1)/(3)(9)=3\ units`

therefore

`VY=6,YX=3`