Question

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

• A. (12, -2)
• B. (10, -3)
• C. (10, -2)
• D. (9, -2)

Answer 1

The correct option is C (10, -2)

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

$\because$ Centroid of a triangle with vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by (x,y) where;

$x$ = $\frac{x_1+x_2+x_3}{3}$ and $y$ = $\frac{y_1+y_2+y_3}{3}$

$\Rightarrow \frac{x+3-7}{3}$ = 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).