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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`.
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 = 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`
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