Question

The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,-6) and (7, 0) is

Answer 1

Given : A triangle with three vertices (0, 6), (8, -6) and (7, 0).

To find : The coordinates of the centroid of the triangle.

Solution :

Let's assume that the coordinates of the centroid of the triangle be (x, y).

Now, coordinates of the centroid of a triangle with given vertices is given by,

$\boxed{\rm (x,y) = \left( \dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3} \right)}$

Here,

• (x1 , y1) = (0, 6)
• (x2, y2) = (8, -6)
• (x3, y3) = (7, 0)

By substituting the values, we get :

$\rm \implies(x,y) = \left( \dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3} \right)$

$\rm \implies(x,y) = \left( \dfrac{0 + 8 + 7}{3},\dfrac{6 - 6 + 0}{3} \right)$

$\rm \implies(x,y) = \left( \dfrac{15}{3},\dfrac{0}{3} \right)$

$\boxed{ \blue{\rm \implies(x,y) = \left( 5,0 \right)}}$

Therefore the coordinates of the centroid of the triangle is (5, 0).