Show that the quadrilateral with vertices `(3, 2), (0, 5), (-3, 2), (0, -1)` is square.

Find the area of the quadrilateral whose vertices are (-4,\ -2),\ (-3,\ -5),\ (3,\ -2),\ (2,\ 3)

Show that the triangle with vertices A (3,5,-4), B (-1, 1,2) C (-5,-5,-2) is isosceles.

Find the area of the quadrilateral whose vertices are : (-4, 5), (0, 7), (5, -5) and (-4, -2)

The area of the quadrilateral formed by the points (1, 2), (2, -3), (-2, 4), (0, 5) is

Show that the DeltaABC with vertices A ( 0,4, 1) , B ( 2, 3, -1) and C ( 4,5,0) is right angled.

Show that the quadrilateral ABCD with A(3,1) ,B(0,-2),C(1,1) and D(4,4) parallelogram.

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)

Statement-1: The quadrilateral whose vertices (in order) are A(1,0), B(0,3) , C(-2,0) and D(0,2) cannot be convex. Statement-2: A quadrilateral ABCD ( in order is) is convex if when any diagonal is taken then the remaining vertices must be on the opposite sides of it.

The centroid of the triangle with vertices (1, sqrt(3)), (0, 0) and (2, 0) is

Show that the points A(2, 1), B(0,3), C(-2, 1) and D(0, -1) are the vertices of a square.