The distance between the points $A(-3, 4)$ and $O(0, 0)$ is $OA = \dots$

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 $AB$.

$A$ point $(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ from $A$,then the ratio of division is $\ldots \ldots \ldots \ldots .$

If one of the end points of the diameter of a circle is $(0,0)$ and the centre of the circle is $(-2,4),$ then the other end point of the diameter is.........

In $\Delta ABC$,if $A(b, c)$,$B(-a, 0)$,and $C(a, 0)$,and $D$ is the midpoint of $\overline{BC}$,then prove that $AB^2 + AC^2 = 2(AD^2 + BD^2)$.

If the vertices of $\Delta ABC$ are $A(-4, -1)$,$B(1, 2)$,and $C(4, -3)$,then the area of the triangle is: