Question

6.The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is *

1 point

(a) (4, 6)

(b) (16/3, 6)

(c) (8, 6)

​

Answer 1

Given : A triangle with three vertices (0, 6), (8, 12) and (8, 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, 12)
• (x3, y3) = (8, 0)

By substituting the values, we get :

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

$\rm \implies(x,y) = \left( \dfrac{0 + 8 + 8}{3},\dfrac{6 +12 + 0}{3} \right)$

$\rm \implies(x,y) = \left( \dfrac{16}{3},\dfrac{18}{3} \right)$

$\boxed{ \blue{\rm \implies(x,y) = \left( \dfrac{16}{3},6 \right)}}$

Therefore option (b) is correct.