The sides of a rectangle are 20 units and 10 units respectively and are parallel to the coordinate axes. If the point of intersection of its diagonals be (4, -2), then find the four vertices of the rectangle.

A(-3, 5) and B(1, 7) are two consecutive vertices of a parallelogram. If the point of intersection of its diagonals be (1, 1), then find its other two vertices.

The sides of the rectangle ABCD are parallel to the coordinate axes. If the coordinates of the vertices B and D be (7,3) and (2,6) respectively , find the coordinates of the vertices A and C .

The sides of the rectangle ABCD are parallel to the coordinate axis. If the coordinates of the vertices B and D be (7,3) and (2,6) respectively, find the coordinates of the vertices A and C .

The ends of a diagonal of a rectangle are (2,3) and (8,11) and its other diagonal is parallel to the axis of y. Find the coordinates of the ends of this diagonal .

The eccentricity of an ellipse is (2)/(3) and the coordinates of its focus and the corresponding vertex are (1,2) and (2,2) respectively. Find the equation of the ellipse . Also find the coordinate of the point of intersection of its major axis and the directrix in the same direction .

If (4,3) , (-2,7) and (0,11) are the coordinates of the mid -points of the sides of a triangle , find the coordinates of its vertices .

P (2, -5), Q(1, -2) and R(4, 7) are the vertices of a triangle. Find the coordinates of the point of intersection of its side PR and the bisector of the angle Q.

A circle passes through the origin O and intersects the coordinate axes at A and B. If the length of diameter of the circle be 3k unit, then find the locus of the centroid of the triangle OAB.

The sides of the rectangle ABCD are parallel to the axes. If the coordinates of A and C are (12, 3) and (7, 6) respectively, find the coordinates of D.

A rectangle has two opposite vertices at the points (1, 2) and (5,5). If the other vertices lie on the line x=3 , find the other vertices of the rectangle.