Question

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. $\infty$

Answer 1

The correct option is A $0$

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.