Q7 of 149 Page 14

Show that the points A (1,- 2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Vertices of a parallelogram ABCD are: A (1,- 2), B (3, 6), C (5, 10) and D (3, 2) Length of side AB =


 


Length of side AB = = √(4+64)= √68 units


 


Length of side BC = = √(4+16) = √20 units


 


Length of side CD = = √(4+64)= √68 units


 


Length of side DA = = √(4+16) = √20 units


 


Length of diagonal BD = = √16= 4 units


 


Length of diagonal AC = = √(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.

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