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प्रश्न
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
उत्तर
AB = `sqrt ((4 + 1)^2 + (6 - 5)^2) = sqrt (25 + 1) = sqrt 26` units
BC = `sqrt ((-1 + 2)^2 + (5 - 0)^2) = sqrt (1 + 25) = sqrt 26` units
CD = `sqrt ((-2 - 3)^2 + (0 - 1)^2) = sqrt (25 + 1) = sqrt 26` units
DA = `sqrt ((3 - 4)^2 + (1 - 6)^2) = sqrt (1 + 25) = sqrt 26` units
AC = `sqrt ((4 + 2)^2 + (6 - 0)^2) = sqrt (36 + 36) = 36 sqrt 2` units
BD = `sqrt ((-1-3)^2 + (5 - 1)^2) = sqrt (36 + 36) = 16 sqrt 2` units
∵ AB = BC = CD = DA and AC ≠ BD
∴ ABCD is a rhombus.
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