Question

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

Answer 1

If point $A(x,-1),B(2,1)$, and $C(4,5)$ are collinear, then slope of $AB$ $=$ slope of $BC$
$\Rightarrow \frac{1-(-1)}{2-x}=\frac{5-1}{4-2}$

$\Rightarrow \frac{1+1}{2-x}=\frac{4}{2}$

$\Rightarrow \frac{2}{2-x}=2$
$\Rightarrow 2=4-2x$

$\Rightarrow 2x=2$

$\Rightarrow x=1$