Find the area of a triangle formed by the points $A(5, 2)$,$B(4, 7)$,and $C(7, -4)$ (in square units).

Find the area of a triangle whose vertices are $(1, -1), (-4, 6)$ and $(-3, -5)$ (in square units).

Prove that the centroid of the triangle with vertices $(1, a), (2, b), (c^2, -3)$ does not lie on the $Y$-axis.

Show that $(-2,-3), (6,3), (3,7),$ and $(-5,1)$ are the vertices of a rectangle.

Find the coordinates of the point $Q$ on the $x$-axis which lies on the perpendicular bisector of the line segment joining the points $A(-5, -2)$ and $B(4, -2)$. Name the type of triangle formed by the points $Q, A$ and $B$.

Students of a school are standing in rows and columns in their playground for a drill practice. $A, B, C$ and $D$ are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students $A, B, C$ and $D$? If so,what should be his position?