Question

A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

Answer 1

A(x₁,y₁) = A(h, -6), 

B (x₂ , y₂) = B(2, 3),

C (x₃ , y₃) = C (-6, k) 

∴ centroid G (x, y) = G (1, 5)

G is the centroid.

By centroid formula,

x = `("x"_1 + "x"_2 + "x"_3)/3`

∴ 1 = `(h + 2 +(-6))/3`

∴ 3 = h + 2 - 6

∴ 3 = h – 4

∴ h = 3 + 4

∴ h = 7

y = `("y"_1 + "y"_2 + "y"_3)/3`

∴ 5 = `(-6 + 3 + "k")/3`

∴ 15 = -3 + k

∴ k = 15 + 3

∴ k = 18

∴ h = 7 and k = 18