Question

Two vertices of a triangle are $P(-4,1)$ and $Q(1,3)$. If the centroid is origin, then the third vertex is

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

Answer 1

Answer: (D)

$(3,-4)$

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