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.

AB = `sqrt((3-6)^2+(4-7)^2)`

= `sqrt((-3)^2+(-3)^2)`

= `sqrt(9+9)`

= `sqrt18`

= `3sqrt2`

BC = `sqrt((6-9)^2+(7-4)^2) `

= `sqrt((-3)^2+(3)^2)`

= `sqrt(9+9)`

= `sqrt18`

= `3sqrt2`

CD = `sqrt((9-6)^2+(4-1)^2)`

= `sqrt((3)^2+(3)^2)`

= `sqrt(9+9)`

= `sqrt18`

= `3sqrt2`

AD = `sqrt((3-6)^2+(4-1)^2)`

= `sqrt((-3)^2 + (3)^2)`

= `sqrt(9+9)`

= `sqrt18`

= `3sqrt2`

Diagonal AC = `sqrt((3-9)^2+(4-4)^2)`

= `sqrt((-6)^2)`

= 6

Diagonal BD = `sqrt((6-6)^2+(7-1)^2)`

= `sqrt((6)^2)`

= 6

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.