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  4. The number of points on the line x + y =4 which are unit distance apart from the line 2 x + 2y = 5 is

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Q. The number of points on the line $x + y =4$ which are unit distance apart from the line $2 x + 2y = 5$ is

WBJEEWBJEE 2009Straight Lines

Solution:

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