Find the distance between the points $A(5, 8)$ and $B(1, 2)$.

Find the coordinates of the point on the $X-$axis which is at a distance of $5$ units from $A(4,4)$.

If $(-8, -4), (-2, 4)$ and $(5, a)$ are collinear points,then find the value of $a$.

Given points $A(3, 4)$ and $B(5, -2)$. Find the point $P(x, y)$ on the plane such that $PA = PB$ and the area of $\Delta PAB = 10$.

$\overline{ AB }$ is given. If $P$ is a point on $\overline{ AB }$ such that $A - P - B$,then $P$ divides $\overline{ AB }$ from $B$ in the division ratio $\ldots \ldots \ldots \ldots$

Find the coordinates of the point $Q$ on the $x$-axis which lies on the perpendicular bisector of the line segment joining the points $A(-5, -2)$ and $B(4, -2)$. Name the type of triangle formed by the points $Q, A$ and $B$.