Question

Two vertices of $△ABC$ are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are

(a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

Answer 1

Two vertices of ΔABCare A(-1,4) and B(5,2). Let the third vertex be C (a, b)

Then the co-ordinates of its centroid are

C= $\frac{(-1+5+a)}{3},\frac{(4+2+b)}{3}$
C= $\frac{4+a}{3},\frac{6+b}{3}$

But it is given that G(0,-3) is the centroid. Therefore

0=$\frac{4+a}{3},-3=\frac{6+b}{3}$

⇒a=-4 , -9-6=b

⇒⇒ a = -4, b = -15

Therefore, the third vertex of ΔABCis C(-4,-15)