Question

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

Answer 1

Answer: 1

We have points $A(x,-1),B(2,1),C(4,5).A,B,C$ are collinear if the
The slope of $AB=$ Slope of $BC$
$\text{Slope of AB}=\left(\frac{y_2-y_1}{x_2-x_1}\right)=\frac{1+1}{2-x}=\frac{2}{2-x}$
$\text{Slope of BC}=\left(\frac{y_2-y_1}{x_2-x_1}\right)=\frac{5-1}{4-2}=\frac{4}{2}=2$
$\therefore \frac{2}{2-x}=2$
$\Rightarrow 2-x=1$
$\Rightarrow x=1$