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

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

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

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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.