Question

By coordinate geometry prove that the line joining the two sides of a triangle is half of the third side. ​

Answer 1

Let, AOB a ∆ in which M and N are the mid points respectively.

Co-ordinate of M = (x/2,y/2)

Co-ordinate of N = (x+a/2,y/2)

MN = √(x+a/2-x/2)² +(y/2 -y/2)²

MN = √(x+a-x/2)² + (y-y/2)²

MN = √(a/2)²

MN = a/2

MN = OB/2