The vertices of a quadrilateral are at `(-2,4)`, `(1,5)`, `(4,3)` and `(1,2)`. Show that this quadrilateral is a parallelogram

The four vertices of a quadrilateral are (1,2),(-5,6),(7,-4) and (k,-2) taken in order.If the area of the quadrilateral is zero,find the value of k.

The vertices of quadrilateral in order are (-1,4),(5,6),(2,9) and (x,x^(2)). The area of the quadrilateral is (15)/(2)sq. Units,then find the point (x,x^(2))

The vertices of quadrilateral ABCD are A(5,-1) B(8,3), C(4,0) and D(1,-4). Prove that ABCD is a rhombus.

Three vertices of a quadrilateral in order are (6,1)(7,2)" and "(-1,0) . If the area of the quadrilateral is 4 sq. unit. Then the locus of the fourth vertex has the equation.

If P(–2, 4), Q(4, 8), R(10, 5) and S(4, 1) are the vertices of a quadrilateral, show that it is a parallelogram.

The vertices of a quadrilateral are A(-4, 2), B(2, 6), C(8, 5) and D(9,-7). Using slopes, show that the midpoints of the sides of the quad. ABCD form a parallelogram.

The area of the quadrilateral whose vertices are (1,2)(6,2),(5,3) and (3,4) , is

The vertices of a quadrilateral in order are (-2,3),(-3,-2) , (2,-1) and (x,y) . If its area is 14 sq. units , then show that x + y = 2.