In a square ABCD, if A and B are (5,1) and (7,1) respectively then what is the locus of the mid point of diagonal AC?

ABCD is a rhombus. The co-ordinates of vertices B and D are (4,7) and (-2,1) respectively . Find the equations of AC.

B (-5, 6) and D (1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at a(4,2). What is the equation of the diagonal BD?

ABCD is a parallelogram in which diagonals AC and BD intereset at O. If E, F, G and H are the mid points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is:

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

E is the mid - point of the diagonal AC of the rectangle ABCD , if the coordinates of A and E are (7,-8) and (2,-2) , then state which of the following are the coordinates of C ?

ABCD is a rhombus. Its diagonals AC and BD intersect at the point M and satisfy BD = 2 AC. If the coordinates of D and M are(1,1) & (2,-1respectively. Then find the coordinates of A

ABCD is a square. E and F are respectively the mid-points of BC and CD. If R is the mid-point of EF, prove that ar (DeltaAER) = ar (DeltaAFR) .