Question

 A (5,3), B(-1,1) and C(7,-3)are the vertices of triangle ABC. If l is the mid-point of AB and M is the mid point of AC, show that LM=1/2BC

Answer 1

I is the mid point of AB,
=(2,2)

M is the midpoint of AC
=(6,0)

Now finding distance LM
=$\sqrt{ 4^{2} + 2^{2} }$ = $\sqrt{20}$

Finding distance BC
=$\sqrt{ 8^{2} + 4^{2} }$ = $\sqrt{80}$ = $2 \sqrt{20}$

Hence prooved that LM=1/2BC