Question

A(h,6) B(2,-2) C(8,k) co-ordinates of vertices of a triangle whose centroid is G(1,3). Find h and k​

Answer 1

solution:

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 = (x1 + x2 + x3)/3

∴ (1 = h + 2 +(-6))/3

∴ 3 = h + 2 - 6

∴ 3 = h – 4

∴ h = 3 + 4

∴ h = 7 y = (y1 + y2 + y3)/3

∴ 5 = (-6 + 3 + k)/3

∴ 15 = -3 + k

∴ k = 15 + 3

∴ k = 18

∴ h = 7 and k = 18