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Question
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
Solution
Since segment AD is median, Point D is the midpoint of side BC.
By midpoint formula,
Co-ordinates of D = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
= `((-3 + 1)/2, (-2 - 8)/2)`
= `((-2)/2, (-10)/2)`
Co-ordinates of D = (–1, – 5)
Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
By distance formula,
d(A, D) = `sqrt([5 - (-1)]^2 + [4 - (-5)]^2`
= `sqrt((5 + 1)^2 + (4 + 5)^2`
= `sqrt(6^2 + 9^2)`
= `sqrt(36 + 81)`
= `sqrt(117)`
∴ The length of segment AD is `sqrt(117)` units.
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