Find the point on the $X$-axis which is equidistant from $(5, 4)$ and $(-2, 3)$.

If the vertices of $\Delta PQR$ are $P(3, 10)$,$Q(6, 5)$,and $R(1, 2)$,then $\Delta PQR$ is a $\dots$ triangle.

Show that the points $A(-2, 1)$,$B(2, -2)$,and $C(5, 2)$ are the vertices of a right-angled triangle.

If $A(4, 3)$ and $B(8, 9)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots \ldots .$

If the midpoint of the line segment joining $P(3, 4)$ and $Q(a, 8)$ is $M(5, 6)$,then $a = \ldots \ldots \ldots \ldots$

$A(6,1), B(8,2)$ and $C(9,4)$ are three vertices of a parallelogram $ABCD$. If $E$ is the midpoint of $DC$,find the area of $\triangle ADE$ (in sq. units).