Question

If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then the third vertex is

• A. (4,8)
• B. (8,4)
• C. (6,4)
• D. (0,0)

Answer 1

The correct option is A

(4,8)

Given:
Centroid = $(4,6)$
Vertices $(6,4)\&(2,6)$

Let the Co-ordinates of $C$ be $(x_3,y_3)$
$x_1=6,x_2=32,y_1=4\&y_2=6$

Centroid $(4,6)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$\Rightarrow 4=\frac{6+2+x_3}{3}$ and $6=\frac{4+6+y_3}{3}$
$\Rightarrow$ $x_3=4$ and $y_3=8$

$\therefore$ Third vertex is $(4,8)$.