Question

The coordinates of the vertices of a triangle ABC are (-2, 1), (5, -3), (7, 8). Find the centroid of the triangle.
1. (10/3, 2)
2. (-10/3, 0)
3. (10/3, -2)
4. (-2, 10/3)

Answer 1

Correct Answer - Option 1 : (10/3, 2)

Given:

Coordinates of the vertices of a triangle ABC = (-2, 1), (5, -3), (7, 8)

Formula Used:

For a triangle with vertices (a, b), (c, d) and (e, f)

Centroid = [(a + c + e)/3, (b + d + f)/3]

Calculations:

Coordinates of the vertices of a triangle ABC = (-2, 1), (5, -3), (7, 8)

⇒ Centroid of triangle ABC = [(-2 + 5 + 7)/3, (1 + (-3) + 8)/3]

⇒ Centroid of triangle ABC = (10/3, 6/3)

⇒ Centroid of triangle ABC = (10/3, 2)

∴ The centroid of the triangle is (10/3, 2).