# 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 - Mathematics

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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

#### 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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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (B) | Q 3 | Page 182