Show that the points (a, a), (-a,-a) and ( − 3 a , 3 a ) are the vertices of an equilateral triangle.
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let A (a, a) B (-a, -a) and C (-3a,3a)
first of all find length AB, BC and AC
now
AB=root {(a+a)^2+(a+a)^2}=root (8a^2)
BC=root {(-a+3a)^2+(-a-3a)^2=root (20a^2)
CA=root {(a+3a)^2+(a-3a)^2}=root (20a^2)
here we see
BC=CA but not equal to AB
so this is not equitatral triangle.
first of all find length AB, BC and AC
now
AB=root {(a+a)^2+(a+a)^2}=root (8a^2)
BC=root {(-a+3a)^2+(-a-3a)^2=root (20a^2)
CA=root {(a+3a)^2+(a-3a)^2}=root (20a^2)
here we see
BC=CA but not equal to AB
so this is not equitatral triangle.
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