Question

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

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 $BC$
$\text{Slope of AB}=\left(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\right)=\frac{1 + 1}{2 - x}=\frac{2}{2 - x}$
$\text{Slope of BC}=\left(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\right)=\frac{5 - 1}{4 - 2}=\frac{4}{2}=2$
$\therefore \frac{2}{2 - x}=2$
$\Rightarrow 2-x=1$
$\Rightarrow x=1$