In each of the following find the value of $k$ , for which the points are collinear.(i) $(7, - 2), (5, 1), (3, k)$

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Solution

Let the points are
$A (7, - 2) B (5, 1) C (3, K)$
For collinearity
$A r e a o f Δ A B C$
$\Rightarrow \frac{1}{2} | 7 (1 - K) + 5 (K + 2) + 3 (- 2 - 1) | = 0$
$\Rightarrow | - 7 - 7 K + 5 K + 10 - 9 | = 0$
$\Rightarrow | - 2 K + 8 | = 0$
$\Rightarrow - 2 K + 8 = 0$
$\Rightarrow 2 K = 8$
$K = 4$

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Similar questions

In each of the following find the value of ‘k’, for which the points are collinear.

(i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)

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For what value of 'k' are the following points (7,-2), (5, 1), (3, k) collinear.

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