Sum

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

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#### Solution

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=4sqrt5`

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

`LM=sqrt(16+4)`

`LM=sqrt(20)`

`LM=2sqrt5`

Hence. `LM=1/2 BC`

Concept: The Mid-point of a Line Segment (Mid-point Formula)

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