Answer:
VY = 16
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 VX at the ratio of 2: 1 from the vertex V
∴ VY: YX = 2: 1
∴ [tex]\frac{VY}{YX}[/tex] = [tex]\frac{2}{1}[/tex]
→ By using cross multiplication
∵ VY × 1 = YX × 2
∴ VY = 2YX
∵ YX = 8
∴ VY = 2(8)
∴ VY = 16
