Question

The third vertex of a triangle, whose two vertices are $(-4,1)$ and $(0,-3)$ and centroid is at the origin is

• A. $(3,1)$
• B. $(-4,1)$
• C. $(4,2)$
• D. $(-1,2)$

Answer 1

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

Centroid of a triangle $=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

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