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

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?

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

If the line $2x - 3y + 4 = 0$ divides the line segment joining the points $A(-2, 3)$ and $B(3, -2)$ in the ratio $m:n$,then the point which divides $AB$ in the ratio $-4m:3n$ is

Find the slope of a line,which passes through the origin and the mid-point of the line segment joining the points $P(0, -4)$ and $B(8, 0)$.

If the distance between the points $(x, 2)$ and $(3, 4)$ is $2$,find the value of $x$.