Question

Find the value of $x$ so that the points $(x,-1),(2,1)$ and $(4,5)$ are collinear.

Answer 1

Let $A(x,-1)B(2,1)$ and $C(4,5)$

They are collinear if slope of $AB=$ slope $BC$

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

Slope of $BC=\frac{5-1}{4-2}=\frac{4}{2}$

$\frac{2}{2-x}=2$

$2-x=1$

$\therefore x=1$