Question

Two vertices of a triangle are the points $(1,4),(7,2)$ and centroid is the point $(5,3)$. Find the coordinates of the third vertex.

• A. $(2,5)$
• B. $(7,2)$
• C. $(3,7)$
• D. $(7,3)$

Answer 1

The correct option is D $(7,3)$

Given vertices of triangle $(1,4),(7,2),(x_3,y_3)$ and $G(5,3)$

In a triangle coordinates of centroid is given by $G(x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.

So,

$5=\frac{1+7+x_3}{3}⟹15=8+x_3⟹x_3=7$

$3=\frac{4+2+y_3}{3}⟹9=6+y_3⟹y_3=3$

Hence $(x_3,y_3)=(7,3)$