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Prove that A (2,-1) B (3,4) …

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Prove that A (2,-1) B (3,4) C (-2,3) D (-3,-2) are the vertices of rhombus ABCD a square?

Posted by Arun Tiwari 6 years, 10 months ago

CBSE > Class 10 > Mathematics

5 answers

Gungun_ ?? 6 years, 10 months ago

Apply distance formula....if all the distances comes equal then it is a square or rhombus....and if the diagonals comes equal then it is square and if diagonals are not equal then it is rhombus

Gaurav Seth 6 years, 10 months ago

By using diatance formula,√ [ (x2 - x1)2 = (y2 - y1)2 ]

AB = √ ( 3 - 2)2 + ( 4 + 1)2 =√ 12 + 52 =√ 1 + 25 =√26 ...1

BC =√ ( -2 -3)2 + ( 3 - 4)2 =√ 25 = 1 =√26 ...2

CD =√ ( -3 + 2)2 + ( -2 -3)2 =√ 25 + 1 =√26 ...3

DA =√(2 + 3)2 + ( -1 + 2)2 =√ 25 + 1 =√ 26 ...4

from 1, 2, 3 and 4

ABCD is a rhombus.

For a rhombus to be a square, diagonals must be equal

So we need to prove that AB = CD

AC =√( -2 - 2 )2 + (3 + 1)2 =√ (-4)2 + (4)2 =√ 16 + 16 =√32

BD =√ (-3 - 3)2 + (-2 - 4)2 =√ (-6)2 + (-6)2 = √ 36 + 36 = √72

Since AC is not equal to BD, it is not a square

Puja Sahoo? 6 years, 10 months ago

Use distance formula......

Puja Sahoo? 6 years, 10 months ago

Dono, diagonal ka length equal hoga

Gungun_ ?? 6 years, 10 months ago

Kiske vertices prove karne hai. ? Rhombus or square?

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