Find the coordinates of the midpoint of the segment whose end points are $A ( 4 , 3 )$ and $B ( 6 , 5 )$

The distance of the point $P$ on the $X-$axis from $A(11, 12)$ is $13$ units. The coordinates of $P$ are $\ldots \ldots \ldots \ldots$.

$A$ 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 $AB^2 + BC^2 + AC^2 = 3(GA^2 + GB^2 + GC^2)$.

Find the area of a triangle having the vertices $A(5, 3)$,$B(4, 5)$,and $C(3, 1)$.

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)