Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $y$-axis.

If $A$ and $B$ are the points $(-3, 4)$ and $(2, 1)$,then the coordinates of the point $C$ on $AB$ produced such that $AC = 2 BC$ are:

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 $k =$

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

If the line segment joining the points $(0, 0)$ and $(3, 4)$ is the hypotenuse of a right-angled triangle,what is the length of the median to the hypotenuse?

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $x$-axis.