Find the area of a triangle having the vertices $A(3, 2), B(11, 8)$ and $C(8, 12)$.

Show that $(0,6), (-5,3)$ and $(3,1)$ are the vertices of an isosceles right triangle.

If $(a, b)$ is the mid-point of the line segment joining the points $A (10, -6)$ and $B (k, 4)$ and $a - 2b = 18$,find the value of $k$ and the distance $AB$.

$\overline{AB}$ is a diameter of a circle having the centre $P$. If $A(5, -6)$ and $B(3, -2)$,then the coordinates of $P = \dots$

$A (1, -2)$ 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 $3AP = 5AB$.

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