In each of the following find the value of '*k*', for which the points are collinear.

(8, 1), (*k*, -4), (2, -5)

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#### Solution

For collinear points, area of triangle formed by them is zero.

Therefore, for points (8, 1), (*k*, - 4), and (2, - 5), area = 0

`1/2 [8 { -4- (-5)} + k{(-5)-(1)} + 2{1 -(-4)}] = 0`

8 - 6*k* + 10 = 0

6*k* = 18

*k* = 3

Concept: Area of a Triangle

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