Q. 5 B5.0( 2 Votes )

Show that the following points form an equilateral triangle.

(a, 0), (−a, 0) and (0, a√3)

Answer :

Formula used:


(a, 0), (–a, 0) and (0, a√3)


Let the points be A (a, 0), B (–a, 0) and C (0, a√3)


Distance of AB


AB = √ ((–a – a)2 + (0 – 0)2)


AB = √ ((–2a)2 + (0)2)


AB = √ (4a2 + 0)


AB = √4a2


AB = 2a


Distance of BC


B C= √ ((0 – a)2 + (a√3 – 0)2)


BC = √ ((–a)2 + (a√3)2)


BC = √ (a2 + 3a2)


BC = √4a2


BC = 2a


Distance of AC


AC = √ ((0 – a)2 + (a√3 – 0))2)


AC = √ ((–a)2 + (a√3)2)


AC = √ (a2 + 3a2)


AC = √ 4a2


AC = 2a


AB = BC = AC = 2a


Since, all the sides are equal the points form an equilateral triangle.


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