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.

From figure,

Co-ordinates of A = (3, 4), B = (6, 7), C = (9, 4) and D = (6, 1).

By formula,

Distance between two points (D) = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Substituting values we get :

$AB = \sqrt{(6 - 3)^2 + (7 - 4)^2} \\[1em] = \sqrt{3^2 + 3^2} \\[1em] = \sqrt{9 + 9} \\[1em] = \sqrt{18} \\[1em] = 3\sqrt{2} \text{ units}. \\[1em] BC = \sqrt{(9 - 6)^2 + (4 - 7)^2} \\[1em] = \sqrt{3^2 + (-3)^2} \\[1em] = \sqrt{9 + 9} \\[1em] = \sqrt{18} \\[1em] = 3\sqrt{2} \text{ units}. \\[1em] CD = \sqrt{(6 - 9)^2 + (1 - 4)^2} \\[1em] = \sqrt{(-3)^2 + (-3)^2} \\[1em] = \sqrt{9 + 9} \\[1em] = \sqrt{18} \\[1em] = 3\sqrt{2} \text{ units} \\[1em] AD = \sqrt{(6 - 3)^2 + (1 - 4)^2} \\[1em] = \sqrt{3^2 + (-3)^2} \\[1em] = \sqrt{9 + 9} \\[1em] = \sqrt{18} \\[1em] = 3\sqrt{2} \text{ units}.$

Since, AB = BC = CD = AD.

∴ ABCD is a square.

Hence, Champa is correct.