(Q29)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 "dont you think ABCD is a square?" phani disagrees. Using distance formula, find which of them is correct.why?
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Answer

Given Four friends are seated at, A,B,C and D where A(3,4) B(6,7) C(9,4) and D(6,1)

Now distance=√((x2 - x1)2 + (y2 - y1)2)

AB=√((-)2 + (-)2)

=√

=√2

BC=√((-)2 + (-)2)

=√

=√2

CD=√((-)2 + (-)2)

=√

=√2

AD=√((-)2 + (-)2)

=√

=√2

AC=√((-)2 + (-)2)

=√

=

BD=√((-)2 + (-)2)

=√

=

Hence in ABCD four sides are equal AB=BC=CD=DA=√2

and two digonals are equal AC=BD=units

∴ ABCD forms a square i.e., jarina is correct