Question

A line passing through $P(2,-3)$ is making an angle ${135}^{\circ }$ in anticlockwise direction with $x-$ axis and is intersecting another line $x+2y-3=0$ at $Q$. Then the length of $PQ$ is

• A. $7\sqrt{2}\text{units}$
• B. $\frac{7}{3\sqrt{2}}\text{units}$
• C. $\frac{1}{3\sqrt{2}}\text{units}$
• D. $3\text{units}$

Answer 1

The correct option is A $7\sqrt{2}\text{units}$

Equation of the line which passes through $P(2,-3)$ and making an angle of $135°$ in anticlockwise direction with $x-$ axis is
$\frac{x-2}{\cos 135°}=\frac{y+3}{\sin 135°}=r\Rightarrow x=2-\frac{r}{\sqrt{2}};y=-3+\frac{r}{\sqrt{2}}$
Now putting the value of $x,y$ in the line
$x+2y-3=0$
$\therefore 2-\frac{r}{\sqrt{2}}-6+\frac{2r}{\sqrt{2}}-3=0\Rightarrow r=7\sqrt{2}$