# the vertex of the triangle to be equilateral

• Jan 7th 2013, 06:41 AM
rcs
the vertex of the triangle to be equilateral
A triangle has two vertices at ( -a, 0 ) and (a , 0 ). What must be the third vertex of the triangle to be equilateral?

Thanks
• Jan 7th 2013, 06:54 AM
Plato
Re: the vertex of the triangle to be equilateral
Quote:

Originally Posted by rcs
A triangle has two vertices at ( -a, 0 ) and (a , 0 ). What must be the third vertex of the triangle to be equilateral?

The third vertex will be $(0,b)$ where the distance $\mathcal{D}[(0.b);(a,0)]=2|a|$
• Jan 7th 2013, 07:07 AM
skeeter
Re: the vertex of the triangle to be equilateral
Quote:

Originally Posted by rcs
A triangle has two vertices at ( -a, 0 ) and (a , 0 ). What must be the third vertex of the triangle to be equilateral?

... note that half an equilateral triangle is a 30-60-90 special right triangle.