If $(-\sqrt{2}, \sqrt{2})$ are the Cartesian coordinates of a point,then its polar coordinates are $.....$

An insect is resting on the graph paper at a point $A(3, 2)$. Now it starts moving towards the west direction and covers a distance of $4 \ units$,then it turns towards the south and covers a distance of $3 \ units$ to reach point $B$. The polar coordinates of point $B$ will be:

Two fixed points are $A(a, 0)$ and $B(-a, 0)$. If $\angle A - \angle B = \theta$,then the locus of point $C$ of triangle $ABC$ will be

The vertices of a figure are $(-2, 2), (-2, -1), (3, -1),$ and $(3, 2)$. This figure is a:

Point $A(5, 12)$ is rotated about the origin $O$ in the $XY$-plane through an angle of $30^\circ$ in the anticlockwise direction to a new position $B$. The ordinate of point $B$ is...

If a square $ABCD$,where $A(0,0), B(2,0), C(2,2)$ and $D(0,2)$ undergoes the following transformations successively,then the final figure would be a:
$(i)$ $f_1(x, y) \longrightarrow (y, x)$
(ii) $f_2(x, y) \longrightarrow (x+3y, y)$
(iii) $f_3(x, y) \longrightarrow \left(\frac{x-y}{2}, \frac{x+y}{2}\right)$