If the polar coordinates of a point are $\left(2, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

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 $k =$

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

The polar coordinates of the point whose Cartesian coordinates are $(-2, -2)$ are given by

If $C$ is the reflection of $A(2, 4)$ in the $x$-axis and $B$ is the reflection of $C$ in the $y$-axis,then $|AB|$ is