show that the points (a,a) , (-a,-a) , (-root3a , root3a) are the vertices of an equilateral triangle.
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use distance formula
let A (a, a), B (-a,-a) andC (-root3.a, root3.a)
now, AB=2root2.a
BC=2root2.a
CA=2root2.a
and also, check collinearity by slope formula .
slope of ABnot equal slope of BC not equal slope of CA
here all side are same length.
so, ABC is equilatral traingle
let A (a, a), B (-a,-a) andC (-root3.a, root3.a)
now, AB=2root2.a
BC=2root2.a
CA=2root2.a
and also, check collinearity by slope formula .
slope of ABnot equal slope of BC not equal slope of CA
here all side are same length.
so, ABC is equilatral traingle
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