Question

Find the centroids of the triangles whose vertices are given below. 

i. (-7, 6), (2,-2), (8, 5)

ii. (3, -5), (4, 3), (11,-4) 

iii. (4, 7), (8, 4), (7, 11)

Answer 1

i. Let A (x₁, y₁) = A (-7, 6),

B (x₂, y₂) = B (2, -2), 

C (x₃, y₃) = C(8, 5)

∴ By centroid formula,

∴ The co-ordinates of the centroid are (1, 3).

ii. Let A (x₁, y₁) = A (3, -5),

B (x₂, y₂) = B (4, 3), 

C(x₃, y₃) = C(11, -4)

∴ By centroid formula,

∴ The co-ordinates of the centroid are (6, -2).

iii. Let A (x₁, y₁) = A (4, 7),

B (x₂, y₂) = B (8, 4), 

C (x₃, y₃) = C(7, 11)

∴ By centroid formula,

∴ The co-ordinates of the centroid are (19/3, 22/3)