Question

The polar coordinate of a point $P$ is $(2,-\frac{\pi }{4})$. The polar coordinate of the point $Q$, which is such that the line joining $PQ$ is bisected perpendicularly by the initial line, is

• A. $(2,\frac{\pi }{4})$
• B. $(2,\frac{\pi }{6})$
• C. $(-2,\frac{\pi }{4})$
• D. $(-2,\frac{\pi }{6})$

Answer 1

The correct option is A $(2,\frac{\pi }{4})$

Considering our regular Cartesian plane $P$ is a point at a distance of $2$ units from origin and making an angle of $-\frac{\pi }{4}$ with the positive x-axis.
The initial line is x-axis.
$PQ$ will be perpendicularly bisected by x-axis if $Q$ is the mirror image of $P$. So, all we need to rotate the point by $+\frac{\pi }{2}$.
Thus, the point $Q$ will have polar coordinate $(2,\frac{\pi }{4})$.