Q. 32 B4.4( 7 Votes )

# Show that the following points are the vertices of a rectangle:A(2, – 2), B(14, 10), C(11, 13) and D(– 1, 1)

AB = √{(14 – 2)2 + (10 – (– 2))2}

= √{144 + 144} = √288

BC = √{(11 – 14)2 + (10 – 13)2}

= √{9 + 9} = √18 units

CD = √{(– 1 – 11)2 + (1 – 13)2}

= √{144 + 144}

= √288 units

DA = √{(– 1 – 2)2 + (1 – (– 2))2}

= √{9 + 9} = √18units

AB = CD and BC = DA

AC = √{(11 – 2)2 + (13 – (– 2))2}

= √{81 + 225}

= √306 units

For a Rectangle

AC2 = AB2 + BC2

Here AC2 = 306

But AB2 + BC2 = 288 + 18 = 306

ABCD is a rectangle

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