Find the point on the $Y$-axis which is equidistant from $(3, 1)$ and $(-2, 5)$.

State whether the following statements are true or false. Justify your answer.
Points $A(4,3), B(6,4), C(5,-6)$ and $D(-3,5)$ are the vertices of a parallelogram.

Show that,for every $a \in R$,the area of the triangle having the vertices $A(5, a)$,$B(2, 5)$,and $C(2, 3)$ is $3$ square units.

$A$ circle drawn with the origin as the center passes through $\left(\frac{13}{2}, 0\right)$. The point which does not lie in the interior of the circle is

If $G$ is the centroid of a triangle having vertices $A(3h, 3k)$,$B(-3a, 0)$,and $C(3a, 0)$,then prove that $AB^2 + BC^2 + AC^2 = 3(GA^2 + GB^2 + GC^2)$.

If the points are $(12, 10)$ and $(0, 8)$,then the midpoint of the line segment joining these two points is $\ldots \ldots \ldots \ldots$