Question

Examine whether the following points taken in order form a square.

(5, 2), (1, 5), ( - 2, 1) and (2, - 2)

Answer 1

Let us consider the given points as A(5,2) ; B(1,5) ; C(-2,1) ; D(2,-2)
The distance b/w AB = √(1-5)²+(5-2)² =√16+9 = 5
The distance b/w BC = √(-2-1)²+(1-5)² = 5
In the same way distance b/w CD = 5 ; DA = 5
The distance b/w AC = √(-2-5)²+(1-2)² =√49+1 =√50
The distance b/w BD = √(2-1)²+(-2-5)² = √50
As the sides are equal AB = BC = CD = DA  
The diagonals are also equal AC= BD
Therefore the given points represents square