Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

Since, points are $A(x,-1),B(2,1)$ and $C(4,5)$ are collinear.
Here, $x_1=x,y_1=-1,x_2=2,y_2=1,x_3=4$ and $y_3=5$
Slope of $AB=$ Slope of $BC$
$\Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$
$\Rightarrow \frac{1+1}{2-x}=\frac{5-1}{4-2}\left(\because \text{ slope of line }=\frac{y_2-y_1}{x_2-x_1}\right)$
$\Rightarrow \frac{2}{2-x}=\frac{4}{2}\Rightarrow 2-x=1$
$\Rightarrow x=2-1=1$