Q. The equations of the lines through (1, 1) and making angle of $45{^\circ}$ 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) $x - 1 = 0,\ y - 1 = 0$
Explanation
(d)
Let $m$ be the slope of required line
$\therefore\left| \frac{m - ( - 1)}{1 + m( - 1)} \right| = 1$
$\Rightarrow \frac{m + 1}{1 - m} = \pm 1$
$\Rightarrow m + 1 = 1 - m,\ m + 1 = - 1 + m$
$\Rightarrow m = 0,\ m = \infty$
$\therefore$ Equation of the line through (1, 1)is $y - 1 = 0,\ x - 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.