In a classroom, 4 friends are seated at the points A, B, C and D as shown in Figure. 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.
From figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).
Find distance between points using distance formula, we get
AB = \(\sqrt{(6-3)^2 + (7-4)^2}\)
= \(\sqrt{9+9}\)
= \(3\sqrt{2}\)
BC = \(\sqrt{(9-6)^2 + (4-7)^2}\)
= \(\sqrt{9+9}\)
= \(3\sqrt{2}\)
CD = \(\sqrt{(6-9)^2 + (1-4)^2}\)
= \(\sqrt{9+9}\)
= \(3\sqrt{2}\)
DA = \(\sqrt{(6-3)^2 + (1-4)^2}\)
= \(\sqrt{9+9}\)
= \(3\sqrt{2}\)
AB = BC = CD = DA = \(3\sqrt{2}\)
All sides are of equal length. Therefore, ABCD is a square and hence, Champa was correct.