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Question

In each of the following find the value of k, for which the points are collinear. 8,1,k,-4 and 2,-5


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Solution

Find the value k

For collinear point, area of triangle formed by them is always zero

Let point 8,1,k,-4 are 2,-5 are vertices of triangle.

Areaoftriangle=12a1b11a2b21a3b31Areaoftriangle=12811k-412-51Areaoftriangle=128-4+5+12-k+1-5k+80=8+2-k-5k+8Forcollinearpointareaoftriangleis00=18-6kk=3

Hence value of k is 3


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