The point on the $y$-axis equidistant from the points $(3, 2)$ and $(-1, 3)$ is

In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

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

What are the coordinates of the points of trisection of the line segment joining the points $(-3, -3)$ and $(6, 6)$?

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 point $A$ divides the join of the points $(-5, 1)$ and $(3, 5)$ in the ratio $k : 1$. The coordinates of the points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively. If the area of the triangle $ABC$ is $2$ square units,then $k =$