Question
Wed March 09, 2011 By: Devansh Mudgal
 

if two vertices of an equilateral triangle are (3,0 and (6,0), find the third vertex.

Expert Reply
Tue March 08, 2011
Dear student,
 
The given vertices are A(3, 0) and B(6, 0).
Let the coordinates of the third vertex be C(x, y).
 
We have AB = BC = CA
AB2 = BC2 = CA2
Using distance formula, we have:
(6-3)+ (0-0)2 = (x-6)2 + (y-0)2 = (x-3)2 + (y-0)2
9 = x2 + 36 - 12x + y2 = x2 + 9 - 6x + y2
Now, consider x2 + 36 - 12x + y2 = x2 + 9 - 6x + y2 and find the value of x from this relation.
 
Then, consider the relation 9 = x2 + 36 - 12x + y2 to get the value of y and thus obtain the third vertex of the equilateral triangle.
 
We hope that clarifies your query.
 
Regards,
Team
TopperLearning
Sun March 26, 2017

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