In a classroom, 4 friends are seated at the points A, B, C and D as shown in the given figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.
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A(3,4),B(6,7),C(9,4),D(6,1)
AB=(6−3)2+(7−4)2=32+32
=9+9=18=32
BC=(9−6)2+(6−7)2=32+(−3)2
=9+9=18=32
CD=(6−9)2+(1−4)2=(−3)2+(−3)2
=9+9=18=32
DA=(6−3)2+(1−4)2=32+(−3)2
=9+9=18=32
Four sides of quadrilateral ABCD are equal to each other.
∵AB=BC=CD=DA=32
Diagonal AC=(9−3)2+(4−4)2=6
Diagonal BD=(6−6)2+(1−7)2=6
Diagonal AC=Diagonal BD
∴ABCD is a square.
∴ Champa is correct among two
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