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Coordinate Geometry | CBSE Online Coaching | NCERT Solution for Class 10 Maths Exercise Question Exercise 7.1 Question 5

It is a moderate difficulty question to check whether the 4 points given in the question form a square.

This question requires the application of two concepts:
1. Distance Formula
2. Condition to check for a square

Question:
In a classroom, 4 friends are seated at the points A, B, C and D. 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 the distance formula, find which of them is correct.

Approach:
1. Let A(3, 4), B(6, 7), C(9, 4) and D(6, 1)
2. Compute the lengths of all 4 sides using the distance formula.
3. Check whether all the sides are equal in length.
4. Compute the lengths of the diagonals AC and BD using the distance formula.
5. Check whether both diagonals are equal in length.
6. If all sides are equal and both diagonals are equal, then ABCD is a square.

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