If the points $(7, - 2), (5, 1)$ and $(3, k)$ are collinear, then find the value of $k$ .

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Solution

Point $A (7, - 2), B (5, 1)$ and $C (3, k)$ are collinear if

Slope of $A B =$ Slope of $B C$
$\frac{1 - (- 2)}{5 - 7} = \frac{k - 1}{3 - 5}$
$\frac{3}{- 2} = \frac{k - 1}{- 2}$
$\Rightarrow k - 1 = 3$
$k = 3 + 1 = 4$

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