Vertices of a parallelogram ABCD are: A (1,- 2), B (3, 6), C (5, 10) and D (3, 2) Length of side AB
= \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Length of side AB = \(\sqrt{(3 - 1)^2 + (6 + 2)^2}\) = \(\sqrt(4 + 64)\)
= \(\sqrt68\) units
Length of side BC = \(\sqrt{(5 - 3)^2 + (10 - 6)^2}\) = \(\sqrt(4 + 16)\)
= \(\sqrt20\) units
Length of side CD = \(\sqrt{(3 - 5)^2 + (2 - 10)^2}\) = √(4 + 64)
= √68 units
Length of side DA = \(\sqrt{(3 - 1)^2 + (2 + 2)^2}\) = √(4+16)
= √20 units
Length of diagonal BD = \(\sqrt{(3 - 3)^2 + (2 - 6)^2}\)
= √16 = 4 units
Length of diagonal AC = \(\sqrt{(5 - 1)^2 + (10 + 2)^2}\) = √(16+144)
= √160 units
Opposite sides of the quadrilateral formed by the given four points are equal i.e. (AB = CD) & (DA = BC)Also, the diagonals BD & AC are unequal.Therefore, the given points form a parallelogram.