7. 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 in order to complete the rhombus ABCD. Measure the
diagonals of this rhombus and check whether they are equal or not.
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(3 , 0) coordinates of the fourth point D , Both diagonals are equal
Step-by-step explanation:
Let say coordinate of D = ( x , y)
A (1, 2), B (3, 4) and C (5,2)
AB = √(3 - 1)² + (4 - 2)² = √4 + 4 = 2√2
BC = √(5 - 3)² + (2 - 4)² = √4 + 4 = 2√2
AD = CD = 2√2
AD² = CD² = 8
AD² = (x - 1)² + (y - 2)² = 8
CD² = (x - 5)² + (y - 2)² = 8
(x - 1)² + (y - 2)² = (x - 5)² + (y - 2)²
=> x² + 1 - 2x = x² + 25 - 10x
=> 8x = 24
=> x = 3
(3 - 1)² + (y - 2)² = 8
=> (y - 2)² = 4
=> y - 2 = ± 2
=> y = 0 , 4
( 3, 4) is point B
Hence (3 , 0) would be D
Diagonal AC = 4
Diagonal BD = 4
Diagonals are equal
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