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
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