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,

F is the midpoint of seg AB.

By midpoint formula,

Adding (i), (iii) and (v),

Adding (ii), (iv) and (vi),

G is the centroid of ∆ABC. 

By centroid formula,

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