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

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of set $A$ is $56$ more than the total number of subsets of set $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2, -3)$ is

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

Write the equations for the $x$-axis and $y$-axis.

The polar coordinate of a point $P$ is $\left(2, -\frac{\pi}{4}\right)$. The polar coordinate of the point $Q$, which is such that the line joining $PQ$ is bisected perpendicularly by the initial line, is

What are the coordinates of the point that divides the line segment joining the points $(-3, -4)$ and $(-8, 7)$ externally in the ratio $7 : 5$?