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प्रश्न
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
उत्तर
AB = `sqrt ((0 - 4)^2 + (3 - 3)^2)` = 4 units
BC = `sqrt ((4 - 2)^2 + (3 - 3 - 2sqrt 3)^2) = sqrt (4 + 12)` = 4 units
AC = `sqrt ((2 - 0)^2 + (3 + 2 sqrt 3 - 3)^2) = sqrt (4 + 12) ` = 4 units
∵ AB = BC = AC
∴ ABC is an equilateral triangle.
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