Question

The points (7, – 6), (2, k) and (h, 18) are the vertices of triangle. If (1, 5) are the coordinates of centroid, find the value of h and k

Answer 1

Let (7, – 6) ≡ (x₁, y₁), (2, k) ≡ (x₂, y₂), (h, 18) ≡ (x₃, y₃) be the three vertices of the triangle.

(1, 5) are coordinates of centroid.

∴ By Centroid formula,

1 = `(x_1 + x_2 + x_3)/3`

∴ 1 = `(7 + 2 + "h")/3`

∴ 3 = 9 + h

∴ h = – 6

5 = `(y_1 + y_2 + y_3)/3`

∴ 5 = `(-6 + "k" + 18)/3`

∴ 15 = 12 + k

∴ k = 3