Question

If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______.

Options

• (12, 9)

• (9, 12)

• (4, 3)

• (3, 4)

Answer 1

If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are (4, 3).

Explanation:

Let P(x₁, y₁), Q(x₂, y₂), R(x₃, y₃) be the co-ordinates of the vertices of a triangle.

Given that x₁ + x₂ + x₃ = 12 and y₁ + y₂ + y₃ = 9

∴ Co-ordinates of the centroid S(x, y) are

`x = (x_1 + x_2 + x_3)/3` and `y = (y_1 + y_2 + y_3)/3`

`x = 12/3` and `y = 9/3`

x = 4 and y = 3

∴ S(x, y) = (4, 3)