Quadrilateral part 7

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 co-ordinates of the four vertices of quadrilateral are (-2,4),(-1,2), (1, 2) and (2, 4), taken in order. The equation of the line through the vertex (-1, 2) and dividing the quadrilateral in two equal parts is:

Angles of a quadrilateral are (4x)^@, 5(x+2)^@, (7x-20)^@ and 6(x+3)^@ . Find: (i) the value of x. (ii) each angle of the quadrilateral.

Two angles of a quadrilateral are 68^@ and 76^@ . If the other two angles are in the ratio 5:7, find the measure of each of them.

The angles of a quadrilateral are in the ratio 3: 4: 5: 6 . Show that the quadrilateral is a trapezium.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral ?

Quadrilateral class 9

The vertices of a quadrilateral are A(-2,6),\ B(1,2),\ C(10 ,4)a n d D(7,8) . Find the equations of its diagonals.