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

Correct option is (c) (4, 2)

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

Let the third vertex of the triangle be (x, y)

So, centroid = \(\left(\frac{-4 + 0 + x}{3}, \frac{1 - 3 + y}3\right) = (0,0)\)

⇒ \(\left(\frac{-4 + x}3, \frac{-2 + y}3\right) = (0,0)\)

⇒ −4 + x = 0; −2 + y = 0

x = 4; y = 2

Hence, the third vertex of the triangle is (4, 2).