In a classroom, 4 friends are seated at the points A, B, C, and D as shown in Fig. 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?"

According to the fig. A(3,4), B(6,7), C(9,4) and D(6,1) are the positions of 4 friends. If we join all these points then
By using distance formula = √(x₂-x₁)² + (y₂-y₁)²
AB = √(3-6)² + (4-7)² = √(-3)² + (-3)² = √9+9 = √18 = 3√2
BC = √(6-9)² + (7-4)² = √(-3)² + (3)² = √9+9 = √18 = 3√2
CD = √(9-6)² + (4-1)² = √(3)² + (3)² = √9+9 = √18 = 3√2
AD = √(3-6)² + (4-1)² = √(-3)² + (3)² = √9+9 = √18 = 3√2
If we join the points AC and BD then
Diagonal AC = √(3-9)² + (4-4)² = √(-6)² + (0)² = √36 = 6
Diagonal BD = √(6-6)² + (7-1)² = √(0)² + (6)² = √36 = 6
Hence all the sides of a quadrilateral are the same and the diagonals are also the same so ABCD is a square.
Hence Champa is correct.