Question

Two vertices of a triangle are $(-2,-3)$ and $(4,-1)$ and centroid is at the origin. The coordinates of the third vertex of the triangle are:

• A. $(-2,3)$
• B. $(-3,-2)$
• C. $(-2,4)$
• D. $(4,-2)$

Answer 1

The correct option is C $(-2,4)$

Centroid of a triangle with vertices ${(x}_1,y_1);{(x}_2,y_2)$ and ${(x}_3,y_3)$
is calculated by the formula $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Let the third vertex of the triangle be $(x,y)$
So, centroid $=(\frac{-2+4+x}{3},\frac{-3-1+y}{3})=(0,0)$
$=(\frac{2+x}{3},\frac{-4+y}{3})=(0,0)$
$=>2+x=0;-4+y=0$
$x=-2;y=4$
Hence the third vertex of the triangle is $(-2,4)$