Determination of the Shape

If four points are given then How to determine whether the shape is a rectangle, square, rhombus or parallelogram.

1)      Plot the points roughly on a grid to determine the vertices.

2)      Make vectors of diagonals.

3)      Also make vectors of   sides.

4)      Take dot product of adjacent side vectors, Call it S.

5)      Take dot product of diagonal vectors, Call it D.

6)      Go according to following table

S	D	Vectors	Shape
If all S are = 0	0	Two pairs of equal side vectors	Square
If all S are = 0	/= 0	Two pairs of equal side vectors	Rectangle
If All S are /= 0	0	Two pairs of equal side vectors	Rhombus
If all S are /= 0	/=0		General Shape
If all S are /= 0	/=0	Two pairs of equal side vectors	Parallelogram
If Some S=0, some not	May or may not =0	No side vector is equal  to another, but Two of unit vectors are equal.	Trapezoid
		No unit vector is equal.	General Quadrilateral

(Note: /= stands for not equal to)

It would be better to learn properties of these shapes. If you do so you can easily figure out the shape even by inspection.

If you locate some error please correct it or mention it in the comments.

Warm Sentiments

Provided by Syed Hashim Shah.