In each of the following find the value of k, for which the points are collinear.(8, 1), (k, – 4), (2,

Engineering

Mathematics

Introduction to Determinants

Question

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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Let the points are

A(8, 1) B(K – 4) C(2, – 5)

For collinearity

Area of ΔABC

\frac{1}{2} ∣ 8 (- 4 + 5) + K (- 5 - 1) + 2 (1 + 4) ∣ = 0

|8 – 6k + 10 = 0|

18 – 6k = 0

6k = 18

k = 3

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