Question

The equations of the lines through $(-1,-1)$ and making angles ${45}^o$ with the line $x+y=0$ are

• A. $x+1=0,x-y=0$
• B. $x-y=0,y+1=0$
• C. $x+y+2=0,y+1=0$
• D. $x+1=0,y+1=0$

Answer 1

The correct option is D $x+1=0,y+1=0$

slope of $y=-x$ is $-1$

$\therefore$ it means ${135}^{\circ }$ with $x$ axis

$\therefore$ the angle made by a line with $x$ axis which is making ${45}^{\circ }$ with $y=-x$ is

$135-{45}^{\circ }$ and $135+{45}^{\circ }\equiv {90}^{\circ }$ and ${180}^{\circ }$

$\therefore$ the equation of the required line is

$y=-1$ or $x=-1$