If the point $P (2,1)$ lies on the line segment joining points $A (4,2)$ and $B (8,4)$,then:

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

Using the distance formula,show that the points $A(-1, 4)$,$B(2, 3)$,and $C(5, 2)$ are collinear.

State whether the following statement is true or false. Justify your answer.
Points $A(-6, 10)$,$B(-4, 6)$,and $C(3, -8)$ are collinear such that $AB = \frac{2}{9} AC$.

State whether the following statement is true or false. Justify your answer.
Point $P (0, -7)$ is the point of intersection of the $y$-axis and the perpendicular bisector of the line segment joining the points $A (-1, 0)$ and $B (7, -6)$.

$A (1, -2)$ and $B (-7, 1)$ are the given points. Find $P$ on the line segment $AB$ such that $P$ lies on the extension of $AB$ (as indicated by $P-A-B$ order,though the condition $3AP = 5AB$ implies $P$ is outside the segment $AB$) and $3AP = 5AB$.