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