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

Answer:Part 1) Option C) TY=18, TW=27Part 2) Option A) VY=6, YX=3Step-by-step explanation:see the attached figure to better understand the problemwe know thatA 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 TWstep 1Find TWwe 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 2Find TYwe 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 1Find VYwe know that[tex]VY=\frac{2}{3}VX[/tex]substitute[tex]VY=\frac{2}{3}(9)=6\ units[/tex]step 2Find YXwe 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]