Question

Show that the points A (2,-2), B (8,4) and C (5,7) and D (-1,1) are the angular points of the rectangular​

Answer 1

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Class 11

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>>Straight lines

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>>Prove that the points (2, - 2), (8, 4),

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Prove that the points (2,−2),(8,4),(5,7), and (−1,1) are the angular points of a rectangle.

Easy

Solution

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Given points

A(2,−2),B(8,4),C(5,7) and D(−1,1)

AC=

(2−5)

2

+(−2−7)

2

=

90

BD=

(8−(−1))

2

+(4−1)

2

=

90

⇒ Diagonals AC and BD are equal. (property of rectangle)

AB=

(2−8)

2

+(−2−4)

2

=

72

CD=

(5−(−1))

2

+(7−1)

2

=

72

AB=CD

Similarly by distance formula

BC=AD

⇒ AB=CD & BC=AD and diagonals are also equal.

⇒ ABCD is a rectangle