Question

If the centroid of the triangle whose vertices are (2, 4), (3, a), (4, 2) is (a, 3), then a = ______.

Answer 1

If the centroid of the triangle whose vertices are (2, 4), (3, a), (4, 2) is (a, 3), then a = 3.

Explanation:

The centroid of vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) is `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`.

Here: x-coordinate = `(2 + 3 + 4)/3`

= `9/3`

= 3

So a = 3.

Check y-coordinate: `(4 + a + 2)/3`

= `(6 + a)/3`

= 3 

⇒ 6 + a = 9

⇒ a = 3

Both agree, so a = 3.