Question

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 thing ABCD is a square?" Chameli disagrees. Using distance formula, find which of them is correct.

Answer 1

Coordinates of points

$A(3,4),B(6,7),C(9,4),D(6,1)$

$AB=\sqrt{(3-6{)}^2+(4-7{)}^2}=\sqrt{9+9}=3\sqrt{2}$ units

$BC=\sqrt{(6-9{)}^2+(7-4{)}^2}=\sqrt{9+9}=3\sqrt{2}$ units

$CD=\sqrt{(9-6{)}^2+(4-1{)}^2}=\sqrt{9+9}=3\sqrt{2}$ units

$DA=\sqrt{(6-3{)}^2+(1--4{)}^2}=\sqrt{9+9}=3\sqrt{2}$ units

Since $AB=BC=CD=DA$

and $AC=\sqrt{(3-9{)}^2+(4-4{)}^2}=6$ units

$DB=\sqrt{(6-6{)}^2+(1-7{)}^2}=6$ units

$AC=DB$

Hence ABCD is a square hence Champa is Right.