Question

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of X-axis is

• A. ${120}^{\circ }$
• B. ${45}^{\circ }$
• C. ${135}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C ${135}^{\circ }$

Equation of a straight line in intercept form is $\frac{x}{a}+\frac{x}{b}=1$
Given, $a=b$
$\Rightarrow \frac{x}{a}+\frac{x}{a}=1$
$\Rightarrow x+y=a$
Comparing it with general equation of the line $y=mx+c$, we get
slope, $m=-1=\tan \theta$
$\Rightarrow \theta ={135}^{\circ }$