Question

The distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along a line x – y + 1 =0 is

• A. 4
• B. 2
• C.
• D.

Answer 1

The correct option is A 4

The slope of the line x – y + 1 = 0 is 1. So, it makes an angle of ${45}^{\circ }$ with x – axis.
The equation of a line passing through (2, 3) and making an angle of ${45}^{\circ }$ is
$\frac{x-2}{cos{45}^{\circ }}=\frac{y-3}{sin{45}^{\circ }}=r$
Coordinates of any point on this line are
$(2+rcos{45}^{\circ },3+rsin{45}^{\circ })or(2+\frac{r}{\sqrt{2}},3+\frac{r}{\sqrt{2}})$
If this point lies on the line 2x – 3y + 9 = 0, then$4+\sqrt{2}r-9-\frac{3r}{\sqrt{2}}+9=0$
$\Rightarrow$ r=4$sqrt2$
Hence, (a) is the Correct Answer.