Q. 54.4( 177 Votes )

# 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

Answer :

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(x_{1, }y_{1}) and B(x_{2}, y_{2}) is given by

D = √(x_{2} - x_{1})^{2 }+ (y_{2 }- y_{1})^{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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