Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

The points of trisection of the line segment joining the points $(0, 3)$ and $(6, -3)$ are:

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

The line $2x + y - 3 = 0$ divides the line segment joining the points $A(1, 2)$ and $B(-2, 1)$ in the ratio $a : b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3a}, -3\right)$ and $Q\left(-3, -\frac{b}{3a}\right)$ in the ratio $p : q$,then $\frac{p}{q} + \frac{q}{p} =$

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