# In a classroom, 4 friends areseated at the points A, B, C and D as shown in Fig. 7.8 Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,“Don’t you think ABCD is asquare?” Chameli disagrees.Using distance formula, findwhich of them is correct

It can be seen that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of 4 friends

distance between two points A(x1, y1) and B(x2, y2) is given by

D = √(x2 - x1)+ (y- y1)2

Hence,

AB = [(3- 6)2 + (4 - 7)2]1/2

=

BC = [(6 - 9)2 + (7- 4)2]1/2

=

CD = [(9- 6)2 + (4- 1)2]1/2

=

AD = [(3 - 6)2 + (4 - 1)2]1/2

=

Diagonal AC = [(3 - 9)2 + (4 - 4)2]1/2

=

= 6

Diagonal BD = [(6- 6)2 + (7- 1)2]1/2

=

= 6

It can be seen that all sides of quadrilateral ABCD are of the same length and diagonals are of the same length

Therefore, ABCD is a square and hence, Champa was correct

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