Question

In the given figure ABCD is rhombus with diagonals AC = 16 cm and BD = 8 cm. Find the coordinates of
A, B, C and D.​

Answer 1

Given: ABCD is rhombus with diagonals AC = 16 cm and BD = 8 cm.

To find: The coordinates of  A, B, C and D.

Solution:

• Now we have given that AC = 16 cm.

• We also know that the diagonals of rhombus bisect each other. So:

             AC = AO + OC

             Here AO = OC.

             AC = 2(AO)

             16 cm/ 2 = AO

             AO = 8 cm = OC.

• Since A and C are 8 cm apart from origin, so :

• A = (-8,0) as the point is on x axis and 8 cm to the left of origin.

• C = (8,0) as the point is on x axis and 8 cm to the right of origin.

• Similarly:

             BD = BO + OD

             Here OB = OD

             BD = 2(OB)

             8 cm / 2 = OB

             4 cm = OB = OD

• Since B and D are 4 cm apart from origin, so :

• B = (0,4) as the point is on y axis and 4 cm to the above of origin.

• D = (0,-4) as the point is on y axis and 4 cm to the below of origin.

Answer:

           So the coordinates are: A = (-8,0), B = (0,4), C = (8,0), D = (0,-4)