Question

Find the co-ordinates of centroid of the triangle if points D (-7, 6), E (8, 5) and F (2, -2) are the mid points of the sides of that triangle.

Answer 1

Suppose A (x₁ , y₁ ), B (x₂ , y₂ ) and C (x₃ , y₃ ) are the vertices of the triangle. 

D (-7, 6), E (8, 5) and F (2, -2) are the midpoints of sides BC, AC and AB respectively.

Let G be the centroid of ∆ABC. 

D is the midpoint of seg BC. 

By midpoint formula,

E is the midpoint of seg AC. 

By midpoint formula,

Adding (i), (iii) and (v), x₂ + x₃ + x₁ + x₃ + x₁ + x₂ = -14 + 16 + 4 

∴ 2x₁ + 2x₂ + 2x₃ = 6 

∴ x₁ + x₂ + x₃ = 3 …(vii) Adding (ii), (iv) and (vi),

y₂ + y₃ + y₁ + y₃ + y₁ +y₂ = 12 + 10 – 4 

∴ 2y₁ + 2y₂ + 2y₃ = 18 

∴ y₁ + y₂ + y₃ = 9 …(viii) 

G is the centroid of ∆ABC. 

By centroid formula,

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