Find the point on the $Y$-axis which is equidistant from the points $(-5, -2)$ and $(3, 2)$.

$A (1, -2)$ and $B (-7, 1)$ are the given points. Find $P$ on the line segment $AB$ such that $P$ lies on the extension of $AB$ (as indicated by $P-A-B$ order,though the condition $3AP = 5AB$ implies $P$ is outside the segment $AB$) and $3AP = 5AB$.

Students of a school are standing in rows and columns in their playground for a drill practice. $A, B, C$ and $D$ are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students $A, B, C$ and $D$? If so,what should be his position?

State whether the following statement is true or false. Justify your answer.
$A$ circle has its centre at the origin and a point $P(5,0)$ lies on it. The point $Q(6,8)$ lies outside the circle.

Find the area of the triangle whose vertices are $(-8, 4), (-6, 6)$ and $(-3, 9).$

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.