Question

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

( - 1, 1), (0, 0), (3, 3) and (2, 4)

Answer 1

Let us consider the points to be A(-1,1); B(0,0)  ; C(3,3) ; D(2,4) 
The distance b/w AB = √(0+1)²+(0-1)² = √2
The distance b/w BC = √(0-3)²+(0-3)² = √9+9 = √18 
The distance b/w CD = √(2-3)² +(4-3)² = √2
The distance b/w DA = √(-1-2)²+(4-1)² = √18
The distance b/w AC = √(3+1)²+(3-1)²=√20
The distance b/w BD = √(2-0)²+(4-0)²=√20
As the opposite sides AB=CD and BC=DA and the diagonals AC=BD
There the quadrilateral which is formed by the points A,B,C,D is a rectangle.
Hence proved. 

Answer 2

yes they form sides of a rectangle