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Question
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.
Solution
The points A(5, 1), B(–2, –3) and C(8, 2m) are collinear.
i.e., Area of ∆ABC = 0
`1/2[x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]` = 0
`1/2[5(-3 - 2m) + (-2)(2m - 1) + 8(1 - (-3))]` = 0
`1/2(-15 - 10m - 4m + 2 + 32)` = 0
`1/2(-14m + 19)` = 0
m = `19/14`
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