Question

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

• A. $4\sqrt{2}$
• B. $4$
• C. $\frac{3}{5}$
• D. $3\sqrt{2}$

Answer 1

The correct option is A

$4\sqrt{2}$

The slope of the line $x–y+1=0$ is $1$. $\Rightarrow m=1\Rightarrow \theta =45°$.

Equation of line passing through $(2,3)$ with $\theta$ = ${45}^0$ is
$\frac{x-2}{\cos 45°}=\frac{y-3}{\sin 45°}$ = r

$\because$ Coordinates are $(2+\frac{r}{\sqrt{2}},3+\frac{r}{\sqrt{2}})$

It lies on
$2x-3y+9=0\Rightarrow 4\sqrt{2}+2r-3r=0\therefore r=4\sqrt{2}$