Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Coordinates 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 $3(2+rcos\theta )+2(3+rsin\theta =17$
$\Rightarrow 6+3r.\frac{1}{\sqrt{2}}+6+2r.\frac{1}{\sqrt{2}}=17$
$\Rightarrow \frac{5}{\sqrt{2}}r=5\Rightarrow r=\sqrt{2}$