Question

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

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

Answer 1

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

Line making an angle ${135}^{\circ }$ in anticlockwise direction with positive direction of $x-$axis, then the slope is
$m=-1$
Equation of line passing through $P(2,-3)$ is
$y+3=-(x-2)\Rightarrow x+y+1=0$
Other line is $x+2y-3=0$
Finding the point of intersection, we get
$Q=(-5,4)$

Hence, the length of $PQ$ is $7\sqrt{2}\text{units}.$