Q. The number of points on the line $x + y = 4$ which are unit distance apart from the line $2x + 2y = 5$ is
A) 0
B) 1
C) 2
D) $\infty$
Explanation
(a)
Given lines are $x + y = 4$ and $2x + 2y = 5$ or $x + y = \frac{5}{2}$
The distance between two parallel lines,
$d = \frac{4 - \frac{5}{2}}{\sqrt{1^{2} + 1^{2}}} = \frac{3}{2\sqrt{2}} = \frac{3\sqrt{2}}{4} > 1$
Hence, no point lies in it.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.