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 = 1/2 BC`.

Answer 1

Given, L is the mid-point of AB and M is the mid-point of AC.

Co-ordinates of L are

`((5 - 1)/2, (3 + 1)/2) = (2, 2)`

Co-ordinates of M are

`((5 + 7)/2, (3 - 3)/2) = (6, 0)`

Using distance formula, we have:

`BC = sqrt((7 + 1)^2 + (3 - 1)^2)`

`BC = sqrt(64 + 16)`

`BC = sqrt(80)`

`BC = 4sqrt(5)`

`LM = sqrt((6 - 2)^2 + (0 - 2)^2)`

`LM = sqrt(16 + 4)`

`LM = sqrt(20)`

`LM = 2sqrt(5)`

Hence, `LM = 1/2 BC`