The mid-point of the line segment joining the points $A(-2, 8)$ and $B(-6, -4)$ is

If $P (9a-2, -b)$ divides the line segment joining $A (3a+1, -3)$ and $B (8a, 5)$ in the ratio $3:1$,find the values of $a$ and $b$.

For given point $A(2, 4)$ and $B(-3, b)$,if $AB = \sqrt{26}$,find the possible values of $b$.

The perpendicular distance of the point $(6, 2)$ from the $X-$ axis is.......

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.

Prove that $A (0,0), B (7,0), C (7,5)$,and $D (0,5)$ are the vertices of a rectangle.