Question

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex. [2 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark

Let the coordinates of the third vertex be (x, y).

We know that the coordinates of the centroid of a triangle whose vertices are

$(x_1,y_1)$,$(x_2,y_2)$ and $(x_3,y_3)$ are

$\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}$

Given points are (3, –5) and (–7, 4) and centroid is (2, –1).

$\Rightarrow \frac{x+3-7}{3}=2$ and $\frac{y-5+4}{3}=-1$

$\Rightarrow x-4=6$ and $y-1=-3$

$\Rightarrow x=10$ and $y=-2$

Thus the coordinates of the third vertex are (10, -2).