In which ratio does the point $P (-4, 3)$ divide the line segment joining the points $A (1, -2)$ and $B (-6, 5)$?

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 $C$.

If $P(x, y)$ is equidistant from the points $A(a+b, b-a)$ and $B(a-b, a+b),$ then prove that $bx = ay.$

Which of the following groups is true for $\square ABCD?$

$1$. $\square ABCD$ is a rhombus.	$a$. $\overline{AC}$ and $\overline{BD}$ bisect each other.
$2$. $\square ABCD$ is a parallelogram.	$b$. $\overline{AC}$ and $\overline{BD}$ bisect each other at right angles.
$3$. $\square ABCD$ is a rectangle.	$c$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other at right angles.
$4$. $\square ABCD$ is a square.	$d$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other.

Points $(3,4), (-1,4)$ and $\ldots \ldots \ldots \ldots$ are collinear.

The area of a triangle with vertices $(a, b+c), (b, c+a)$ and $(c, a+b)$ is