Q. 605.0( 5 Votes )

Locate the points A(1,2), B(3,4) and C(5,2) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D to complete the rhombus ABCD. Measure the diagonals of this rhombus and find whether they are equal or not.

Answer :

The points on the graph are

A = (1, 2)


B = (3, 4)


C = (5, 2)



The incomplete rhombus on the graph will look like



The completed rhombus ABCD on the graph is



The coordinates of point D to complete the rhombus ABCD are D (3, 0).


The diagonal AC has the y-coordinate constant, i.e. 2.


The length of AC = difference in x-coordinates = 5 – 1 = 4 units


The diagonal BD has the x-coordinate constant, i.e. 3.


The length of BD = difference in y-coordinates = 4 – 0 = 4 units


The two diagonals of rhombus ABCD are equal in length.


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