Question

Two vertices of a triangle are (2, –4) and (–8, 5). If its centroid is (1, 0), then the coordinates of the third vertex are .

• A. (9, –1)
• B. (8, –1)
• C. (9, –2)
• D. (8, –2)

Answer 1

The correct option is A (9, –1)

Coordinates of the centroid of a triangle whose vertices are $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ are given by $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$
Given, two vertices of a triangle are (2, –4) and (–8, 5) and its centroid is (1, 0).
Let the third vertex be $(x,y)$. Then,

$1=\frac{(2–8+x)}{3}$
$\Rightarrow -6+x=3$
$\Rightarrow x=9$

Similarly, $0=\frac{(-4+5+y)}{3}$
$\Rightarrow 1+y=0$
$\Rightarrow y=–1$

Hence the coordinates of the third vertex are (9, –1).