Question

Find the value of K so that points (7,-2),(5,1) and (3,K) are collinear.

Answer 1

Three points are collinear if they lie on the same line.

Here, A:(7,-2), B:(5,1) and C:(3,K) are collinear, so the slope of AB and BC must be equal.

Slope of AB $=\frac{1-(-2)}{5-7}=\frac{-3}{2}$

Slope of BC $=\frac{K-1}{3-5}=\frac{1-K}{2}$

Thus, $\frac{1-K}{2}=\frac{-3}{2}\Rightarrow 1-K=-3\Rightarrow K=1+3=4$