Show that the points A(1, 2), B(1, 6), C(1 + 2√3, 4) are vertices of an equilateral triangle.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: AB = BC = AC = 4, so ΔABC is equilateral.

\[AB=\sqrt{0^2+4^2}=4\]

\[BC=\sqrt{(2\sqrt3)^2+(4-6)^2}=\sqrt{12+4}=4\]

\[AC=\sqrt{(2\sqrt3)^2+(4-2)^2}=\sqrt{12+4}=4\]

All three sides are equal, so A, B, C are vertices of an equilateral triangle.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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