Prove that the points A(2, 4), B(2, 6) and C(2 + √3, 5) are the vertices of an equilateral triangle.
For an equilateral triangle
AB = BC = AC
AB = √{(6 – 4)2 + (2 – 2)2}
= √{(2)2 + 0}
= √{4 + 0}
= √{4} = 2 units
BC = √{(2 + √3 – 2)2 + (5 – 6)2}
= √{3 + (– 1)2}
= √{4} = 2 units
AC = √{(2 + √3 – 2)2 + (5 – 4)2}
= √{3 + (– 1)2}
= √{4} = 2 units
Hence , AB = BC = AC
∴ ABC is an equilateral triangle.
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