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Question
Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1)
Solution
AD is the median of the ΔABC
D is the mid-point of BC
Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
Mid−point of BC = `((1 + 5)/2, (-1 + 1)/2)`
= `(6/2, 0/2)`
= (3, 0)
Length of the median AD = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((3 + 1)^2 + (0 - 3)^2`
= `sqrt(4^2 + (-3)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5 units
Length of the median AD is 5 units.
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