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Question

Prove that the points A(2, 4), B(2, 6) and C2+3, 5 are the vertices of an equilateral triangle.

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Solution

The given points are A(2, 4), B(2, 6) and C2+3, 5. Now
AB=2-22+4-62=02+-22 =0+4=2BC=2-2-32+6-52=-32+12 =3+1=2
AC=2-2-32+4-52=-32+-12 =3+1=2
Hence, the points A(2, 4), B(2, 6) and C2+3, 5 are the vertices of an equilateral triangle.

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