If the polar coordinates of a point are $(2, \pi /3)$,find its Cartesian coordinates.

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?

The ratio in which the $x$-axis divides the line segment joining the points $(2, -3)$ and $(5, 6)$ is

Points $Q, R,$ and $S$ lie on the line segment joining $P(a, x)$ and $T(b, y)$ such that $PQ = QR = RS = ST$. If $L\left( \frac{5a + 3b}{8}, \frac{5x + 3y}{8} \right)$ is a point on the segment,then $L$ is the midpoint of which line segment?

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

What is the distance between the points $P(a \cos \alpha, a \sin \alpha)$ and $Q(a \cos \beta, a \sin \beta)$?