Question

The line $PQ$ whose equation is $x-y=2$ cuts the $x-$axis at $P$ and $Q$ and passes through$(4,2)$. The line $PQ$ is rotated about $P$ through ${45}^o$ in the anticlockwise direction. The equation of the line $PQ$ in the new position is

• A. $y=-\sqrt{2}$
• B. $y=2$
• C. $x=2$
• D. $x=-2$

Answer 1

The correct option is C $x=2$

$m_{PQ}=\frac{2-0}{4-2}=1$
Now, PQ is rotated through ${45}^o$ about P in anticlockwise direction
$\therefore$ slope of PQ becomes infinity.
$\therefore$ Equation of PQ in new position is $x=2$