Question

The number of points on the line x + y = 4 which are at a unit distance from the line 2x + 2y = 11 is ___________.

Answer 1

Since 2x + 2y = 11 cab be expressed as $x+y=\frac{11}{2}$ which is parallel to x + y = 4.
Distance between these two lines is

$\frac{\left|4-{\displaystyle \frac{11}{2}}\right|}{\sqrt{1+1}}=\frac{\left|{\displaystyle \frac{8-11}{2}}\right|}{\sqrt{2}}=\frac{3}{2\sqrt{2}}=1.06>1$

Hence infinite number of point lie on x + y = 4.