Prove that the line segment joining the middle points of two sides of a triangle is half the third side.

We take O as the origin and OX and OY as the x and y axis respectively.

Let BC = 2a, then B = (-a, 0) and C = (a, 0)

Let A = (b, c), if E and F are the midpoints of sides AC and AB respectively.

Coordinates of midpoint of AC are

Coordinates of the midpoint of AB are

Now, distance between F and E is

d(F,E) = √(x₂ – x₁)² + (y₂ – y₁)²

= a …(i)

and Length of BC = 2a …(ii)

From (i) and (ii), we can say that

Hence Proved