# 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

**Solution:**

The points are located on the graph below along with the fourth point.D

The fourth point is D and the coordinates of that point is (3,0) but that will form a rhombus but with sides AB = BC = CD = DA =√8 and AC = B The length of the diagonals are :

AC = √[(5-1)² + (2-2)²] = √16 = 4

BD = √[(3-3)² + (4-0)²] = √16 = 4

Hence the diagonals AC and BD are equal..

**✦ Try This: **Locate the points A(2,2), B (4,4) and C (6,2) 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.

The graph below shows the rhombus ABCD

The fourth point D is (4,0)

The length of the diagonals are :

AC = √[(6-2)² + (2-2)²] = √16 = 4

BD = √[(4-4)² + (4-0)²] = √16 = 4

The lengths of the two diagonals are equal.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 15

**NCERT Exemplar Class 8 Maths Chapter 12 Problem 60**

## 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

**Summary:**

The fourth point D which completes the rhombus is D and its coordinates are (3,0) and its diagonals AD and BC are equal

**☛ Related Questions:**

- Locate the points P (3,4), Q (1,0), R (0,4), S (4,1) on a graph sheet and write the coordinates of t . . . .
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