Question

In a classroom, 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 think ABCD is a square?” Phani disagrees.
Using distance formula, find which of them is correct. Why?

Answer 1

Solution :

Given points are A(3,4), B(6,7),

C(9,4) and D(6,1)

****************************************

Distance between (x1,y1) , ( x2 ,y2 )

= √ ( x2 - x1 )² + ( y2 - y1 )²

*****************************************
i ) Distance between A and B

= √ ( 6 - 3 )² + ( 7 - 4 )²

= √ 3² + 3²

= √ 9 + 9

AB = √18

ii ) Distance between B and C

= √ ( 9 - 6 )² + ( 4 - 7 )²

= √ 3² + 3²

= √ 9 + 9

BC = √18

iii ) Distance between C And D

= √ ( 6 - 9 )² + ( 1 - 4 )²

= √ 9 + 9

BC = √18

iv ) Distance between D and A

= √( 3 - 6 )² + ( 4 - 1 )²

= √ 9 + 9

DA = √18

v ) Distance between A and C

= √ ( 9 - 3 )² + ( 4 - 4 )²

= √ 36

AC = 6 units

vi ) Distance between B and D

= √ ( 6 - 6 )² + ( 1 - 7 )²

= √ 36

BD = 6 units

Therefore ,

AB = BC = CD = DA

and

AC = BD

Jarina's answer is correct

ABCD becomes a Square.

***

Answer 2

Answer

Given points are A(3,4), B(6,7),C(9,4) and D(6,1)

Distance between (x1,y1), (x2,y2)

= √(x2-x1)² + (y2 - y1)²

---------------------------------

(i) Distance between A and B

= √ (6-3)² + (7-4)²

= √ 3²+3²

= √9+9

AB=√18

ii) Distance between B and C

=√(9-6)²+(4-7) 2

= √3² + 3²

= √9+9

BC = √18

iii) Distance between C And D

=√(6-9)²+(1-4)²

= √9+9

BC = √18

iv) Distance between D and A

=√(3-6)2+(4-1)2

= √9+9

DA = √18

v) Distance between A and C

=√(9-3)²+(4-4)²

= √ 36

AC = 6 units

v) Distance between B and D

=√(6-6)²+(1-7)²

= √ 36

BD = 6 units

Therefore,

AB= BC = CD = DA

and

AC = BD

Jarina's answer is correct

Jarina's answer is correctABCD becomes a Square.