Question

Find the value of $K$, for which the given points are collinear:
$\begin{array}{c}A\\ (7,-2)\end{array}\begin{array}{c}B\\ (5,1)\end{array}\begin{array}{c}C\\ (3,K)\end{array}$

Answer 1

As the three points are collinear: $AB+BC=CA$ and $AB$ and $AC$ will have the same slope.

Slope of $AB=\frac{-2-1}{7-5}$ (1)

Slope of $AB=\frac{-2-K}{7-3}$ (2)

Equating (1) and (2) gives

$\frac{-3}{2}=\frac{-2-K}{4}$

$3=\frac{2+K}{2}$

$6=2+K$

Hence $K=4$