Find the ratio in which the point $P(-2, 3)$ divides the line segment joining $A(4, -9)$ and $B(-3, 5)$ starting from $A$. (in $: 1$)

If $(-4,3)$ and $(4,3)$ are two vertices of an equilateral triangle,find the coordinates of the third vertex,given that the origin lies in the interior of the triangle.

The area of a triangle having vertices $A(0,0), B(4,0)$ and $C(0,6)$ 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 distance between $A(1, 3)$ and $B(a, 0)$ is $3$ units,then $a = \ldots$

In which ratio does the point $P (2, b)$ divide the line segment joining $A (1, 2)$ and $B (4, 5)$ from $A$? Also,find the value of $b$.