Question

A straight line is such that it has distance of $5$ units from the origin and its inclination is ${135}^{\circ }$. The intercepts of the line on the co-ordinate axes are :

• A. $5,5$
• B. $\sqrt{2},\sqrt{2}$
• C. $5\sqrt{2},5\sqrt{2}$
• D. $\frac{5}{\sqrt{2}},\frac{5}{\sqrt{2}}$

Answer 1

Answer: (C)

$5\sqrt{2},5\sqrt{2}$

$\theta =$ inclination of line $={135}^{\circ }$

$\therefore m=\tan \theta =\tan {135}^{\circ }=-1$

$\therefore$ equation of line is $y=-x+c$

And as given- straight line is at distance of $5$ units from origin

$\therefore |\frac{c}{\sqrt{2}}|=5$

$c=+5\sqrt{2},-5\sqrt{2}$

$\therefore y=-x+5\sqrt{2}$ is a equation of straight line

$\therefore$ Intercepts of co ordinate axes are $5\sqrt{2}$ and $5\sqrt{2}$