Distance Formula CBSE NCERT solutions Chapter 7 Exercise 7.1 Question 5
5. In a classroom, 4 friends are seated at the points A (3, 4), B (6, 7), C (9, 4) and D (6, 1). 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.
We have A = (3,4), B = (6, 7), C = (9, 4) and D = (6, 1)
Using Distance Formula to find distances AB, BC, CD and DA, we get
Therefore, All the sides of ABCD are equal here. (1)
Now, we will check the length of its diagonals.
So, Diagonals of ABCD are also equal. (2)
From (1) and (2), we can definitely say that ABCD is a square.
Therefore, Champa is correct.