Question

If two vertices of a triangle (2,– 7),(3,5) and centroid is the origin then third vertex is

Answer 1

Two vertices of a triangle :- (2,– 7) and (3,5)

Coordinates of centroid = (0,0)

Let third vertex of triangle be (a,b)

Now , according to the question :-

$\sf \implies \bigg(\dfrac{2 + 3 + a}{3} ,\dfrac{ - 7+ 5 + b}{3}\bigg) = (0, 0)$

$\sf \implies\dfrac{2 + 3 + a}{3} = 0$

$\sf \implies{2 + 3 + a} = 0 \times 3$

$\sf \implies{5+ a} =0$

$\sf \implies{ a} = - 5$

Now , we will find the value of b. :-

$\sf \implies \dfrac{ - 7+ 5 + b}{3} = 0$

$\sf \implies { - 7+ 5 + b} = 0 \times 3$

$\sf \implies { - 7+ 5 + b} = 0$

$\sf \implies { - 2 + b} = 0$

$\sf \implies { b} =2$

Therefore, value of a = -5 and Value of b = 2

So, coordinates of third vertex = (-5,2)

Answer : (-5,2)