Name the quadrilateral formed, if any, by the following points, and give reasons for your answers:

(i) A (-1, - 2), B (1, 0), C (-1, 2), D (-3, 0)

(ii) A (-3, 5), B (3, 1), C (0, 3), D (-1, - 4)

(iii) A (4, 5), B (7, 6), C (4, 3), D (1, 2)

(i) A (-1, - 2), B (1, 0), C (-1, 2), D (-3, 0)

Using distance formula =

AB = = = units

BC = = = units

CD = = = units

DA = = = units

AB = BC = CD = DA

BD = = = 4 units

AC = = = 4 units

All the four sides of the quadrilateral are equal and diagonals are of equal length. Therefore, the given vertices form a square.

(ii) A (-3, 5), B (3, 1), C (0, 3), D (-1, - 4)

Using distance formula =

AB = = = units

BC = = = units

CD = = = units

DA = = = units

Since all sides are of different length, therefore it is not a particular type of quadrilateral.

(iii) A (4, 5), B (7, 6), C (4, 3), D (1, 2)

Using distance formula =

AB = = = units

BC = = = units

CD = = = units

DA = = = units

Coordinates of midpoint of diagonal AC = X = , Y =

Therefore coordinates of midpoint of AC are (4, 4)

Coordinates of midpoint of diagonal BD = X = , Y =

Therefore coordinates of midpoint of AC are (4, 4)

Since diagonals bisect each other at same point therefore quadrilateral is a parallelogram.