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.

Question

Filo · Accepted Answer

Solution: As per the given figure, 4 points are:

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

Using distance formula,

A B = (6 - 3)^{2} + (7 - 4)^{2} = 18 = 32

B C = (9 - 6)^{2} + (4 - 7)^{2} = 18 = 32

C D = (6 - 9)^{2} + (1 - 4)^{2} = 18 = 32

D A = (6 - 3)^{2} + (1 - 4)^{2} = 18 = 32

It means all sides are equal.
Now, we will check diagonals.

A C = (9 - 3)^{2} + (4 - 4)^{2} = 6

B D = (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.

Question Text	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.
Answer Type	Text solution:1
Upvotes	150

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.

Text solutionVerified

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