Question

11. UZ, VX, and TW are medians of Triangle TUV. If UZ = 21, find UY.​

Answer 1

Answer:

UY = 14

Step-by-step explanation:

• The median of a triangle is the segment that joins a vertex and the midpoint of the side opposite to this vertex.

• The point of intersection of the medians of a triangle, divide each median at ratio 2: 1 from the vertex

In the given figure

∵ TUV is a triangle

∵ UZ, VX, and TW are medians

∵ UZ ∩ VX ∩ TW at point Y

∴ Y is the point of intersection of the 3 medians

→ By using the 2nd rule above

∵ The point Y divide UZ at the ratio of 2: 1 from the vertex U

∴ UY: YZ = 2: 1

∴ $\frac{UY}{YZ}$ = $\frac{2}{1}$

→ By using cross multiplication

∵ UY × 1 = YZ × 2

∴ UY = 2YZ

∵ UZ = UY + YZ

∴ UZ = 2 + 1 = 3 parts

∵ UY = 2 parts

∴ $\frac{UY}{UZ}$ = $\frac{2}{3}$

→ Multiply both sides by UZ

∴ UY =  $\frac{2}{3}$ UZ

∵ UZ = 21

∴ UY =  $\frac{2}{3}$ (21)

∴ UY = 14