Question

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

Answer 1

It can be observed that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of these 4 friends.

$\mathrm{CD}=\sqrt{{\left(9-6\right)}^2+{\left(4-1\right)}^2}=\sqrt{{\left(3\right)}^2+{\left(3\right)}^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$

It can be observed that all sides of this quadrilateral ABCD are of the same length and also the diagonals are of the same length.

Therefore, ABCD is a square and hence, Champa was correct