Question

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In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.?



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Answer 1

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Answer 2

Given :- A Diagram

To find:- The position of ABCD is a square or not.

${\huge{\red{\underline{\underline{Solution:-}}}}}$

The coordinates of -

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

★Distance between points AB

AB= √(6-3)² +(7-4)²

= √18

= 3√2

★Distance between points BC

BC =√ (9-6)² + (4-7)²

= √18

= 3√2

★Distance between points CD,

CD =√ (6-9)² + (1-4)²

= √18

= 3√2

★Distance between points DA,

DA =√ (6-3)² + (1-4)²

= √18

= 3√2

It means all sides are equal.

Now, we will check diagonals.

AC = √( 9-3 )² + (4-4)² = 6

BD = √ ( 6-6)² + (7-1)² = 6.

➟So , Diagonals are also equal .

As, both sides and diagonals are equal.

➟ It is a Square.

➟As, champa was saying, "it is a square", she is correct

Formula used:

Distance formula- √ (x₂ -x₁)² + (y₂-y₁)²

where,

• d= distance
• (x₁ y₁) = coordinates of the first point
• (x₂, y₂) = coordinates of the second point

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