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Question
Show that the points (-3 ,3), (3, 3) and (−3√3,3√3 ) are the vertices of an equilateral triangle.
Show that the points (-3 ,3), (3, 3) and (−3√3,3√3 ) are the vertices of an equilateral triangle.
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Solution
The given points are A (-3,-3), B(3,3) and C(−3√3,3√3). Now,
AB =√[(−3−3)^2+(−3−3)^2]
= √[(−6)^2+(−6)^2]
= √(36+36)=√72 = 6√2
BC = √[(3+3√3)^2+(3−3√3)^2]
=√[9+27+18√3+9+27−18√3]
= √72=6√2
AC =√[(−3+3√3)^2+(−3−3√3)^2]
=√[9+27−18√3+9+27+18√3]
= √72= 6√2
AB=BC=AC
Hence the given points are the vertices of an equilateral triangle
The given points are A (-3,-3), B(3,3) and C(−3√3,3√3). Now,
AB =√[(−3−3)^2+(−3−3)^2]
= √[(−6)^2+(−6)^2]
= √(36+36)=√72 = 6√2
BC = √[(3+3√3)^2+(3−3√3)^2]
=√[9+27+18√3+9+27−18√3]
= √72=6√2
AC =√[(−3+3√3)^2+(−3−3√3)^2]
=√[9+27−18√3+9+27+18√3]
= √72= 6√2
AB=BC=AC
Hence the given points are the vertices of an equilateral triangle
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