Question

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

Answer 1

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)2 + (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.