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.