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.
Provided by Syed Hashim Shah.
Too much time taking , but as a General solution.Good..
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