Question

5. In a class room, 4 friends are seated at the points
A, B, C and D as shown in Figure. Jarina and Phani
walk into the class and after observing for a few
minutes Jarina asks Phani “Don't you notice that
ABCD is a square?” Phani disagrees.
Using distance formula, who is correct. Why?​

Answer 1

Answer:

ANSWER

According to the fig. A(3,4),B(6,7),C(9,4) and D(6,1) are the position of 4 friends .

If we join all these points then

By using distance formula

=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

AB=

(3−6)

2

+(4−7)

2

=

(−3)

2

+(−3)

2

=

9+9

=

18

=3

2

BC=

(6−9)

2

+(7−4)

2

=

(−3)

2

+(3)

2

=

9+9

=

18

=3

2

CB=

(9−6)

2

+(4−1)

2

=

(3)

2

+(3

2

)

=

9+9

=

18

=3

2

AD=

(3−6)

3

+(4−1)

2

=

−3)

2

+(3)

2

=

9+9

=

18

=3

2

if we join the point AC and BD than

DiagonalAC=

(3−9)

2

+(4−4)

2

=

(−6)

2

+(0)

2

=

36

=6

Diagonal BD=

(6−6)

2

+(7−1)

2

=

(0)

2

+(6)

2

=

36

=6

Hence all the sides of a quadrilateral are the same and the diagonals are also the same so ABCD is a square.

Hence Champa is correct.

solution