Question

25. Z is the centroid of TriangleABC. If AZ = 12, what is ZY?

Answer 1

Solution

step 1:

The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

Step 2

use the diagram below to answer the question:

Step 3

$\begin{gathered} AZ\text{ = 12} \\ AZ\text{ = }\frac{2}{3}AY \\ \\ 12\text{ = }\frac{2}{3}AY \\ 2AY\text{ = 3}\times12 \\ \\ 2AY\text{ = 36} \\ \\ AY\text{ = }\frac{36}{2} \\ \\ AY\text{ = 18} \end{gathered}$

Step 4

$\begin{gathered} ZY\text{ = }\frac{1}{3}\text{ AY} \\ \\ ZY\text{ = }\frac{1}{3}\text{ }\times\text{ 18} \\ \\ ZY\text{ = 6} \end{gathered}$

Final answer

(A) 6