The area of a triangle with vertices $A (3,0), B (7,0)$ and $C (8,4)$ is

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 $G$ is the centroid of a triangle having vertices $A(3h, 3k)$,$B(-3a, 0)$,and $C(3a, 0)$,then prove that $AB^2 + BC^2 + AC^2 = 3(GA^2 + GB^2 + GC^2)$.

$A(k, 2)$ and $B(3, 5)$ are the given points. If the point $P(t, t)$ divides the line segment $\overline{AB}$ in the ratio $k:1$ starting from $A$,find the value of $k$.

Name the type of triangle formed by the points $A (-5, 6)$,$B (-4, -2)$,and $C (7, 5)$.

Area of $\Delta ABC$ is $\frac{3}{2}$. The $Y$-coordinate of its centroid is $8$ less than three times its $X$-coordinate. If $A$ is $(2, -3)$ and $B$ is $(3, -2)$,find the coordinates of $C$.