Question

The distance of the point $(2,3)$ from the line $3x+3y=17,$ measured parallel to the line $x-y=4$ is

• A. $4\sqrt{2}$
• B. $5\sqrt{2}$
• C. $\sqrt{2}$
• D. none of these

Answer 1

Answer: (C)

$\sqrt{2}$

Coordinate of any point on the line through $(2,3)$ and parallel to the line $x-y=4$, at a distance $r$, are
$(2+r\cos \theta ,3+r\sin \theta ),$ where $\tan \theta =1.$
If this point lies on the line $3x+2y=17,$
then $3(2+r\cos \theta )+2(3+r\sin \theta )=17$
$\Rightarrow 6+3r.\frac{1}{\sqrt{2}}+6+2r.\frac{1}{\sqrt{2}}=17\Rightarrow \frac{5}{\sqrt{2}}r=5$
$\Rightarrow r=\sqrt{2}.$