Q. 6 B

Show that the following points taken in order form the vertices of a parallelogram.

(9, 5), (6, 0), (2, 3) and (1, 2)

Answer :

Formula used:


(9,5), (6, 0), (–2, –3) and (1, 2)


Let A, B, C and D represent the points (9, 5), (6, 0), (–2, –3) and (1, 2)


Distance of AB


AB = √ ((6 – 9))2 + (0 – 5)2)


AB = √ ((–3)2 + (5)2)


AB = √ (9 + 25)


AB = √ 34


Distance of BC


BC= √ ((–2 – 6)2 + (–3 – 0)2)


BC = √ ((–8)2 + (–3)2)


BC = √ (64 + 9)


BC = √73


Distance of CD


CD = √ ((1 – (–2))2 + (2 – (–3))2)


CD = √ ((1 + 2)2 + (2 + 3))2)


CD = √ ((3)2 + (5)2)


CD = √ (9 + 25)


CD = √36


Distance of AD


AD = √ ((1 – 9))2 + (2 – 5)2)


AD = √ ((–8)2 + (–3)2)


AD = √ (64 + 9)


AD = √ 73


So, AB = CD = √36 and BC = AD = √73


i.e., The opposite sides are equal. Hence ABCD is a parallelogram.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Coordinate Geometry45 mins
Basics of Coordinate Geometry43 mins
A Solid Grip on Basics of Coordinate Geometry49 mins
Quiz | Imp. Qs. of Coordinate Geometry46 mins
NCERT | Coordinate Geometry43 mins
Basic Understanding of Coordinate GeometryFREE Class
Champ Quiz | 2-Dimension( Coordinate geometry )36 mins
Know How to Solve Complex Geometry Problems!27 mins
Euclid's Geometry51 mins
Quiz | Euclid's Geometry44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses