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If Z is the centroid of triangle LMN, WZ=4, ZN=14, and ZY=10, find ZM.

User MattMatt
by
4.1k points

2 Answers

12 votes

Answer:

Explanation:

ZM=8

WM=12

XZ=7

XN=21

LZ=20

User Vrakfall
by
4.7k points
10 votes

Answer:

ZM = 8

Explanation:

A triangle is a polygon shape with three sides and three angles.

The centroid of a triangle is the point of congruency of the median of the triangle sides. The centroid of a triangle (also known as the center of gravity) is located inside the triangle.

The centroid theorem for a triangle states that the centroid is located two-third of the distance from each vertex of the triangle to the midpoint of the opposite side.

ZM = (2/3)WM (centroid theorem)

Therefore: WZ + ZM = WM

WZ = WM - ZM

WZ = WM - (2/3)WM

WZ = (1/3)WM

WM = 3WZ = 3 * 4 = 12

ZM = (2/3) * WM = 2/3 * 12 = 8

User Bazman
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3.8k points