Question

If the points (0, 0), (2, 2$\sqrt{3}$) and (a, b) be the vertices of an equilateral triangle, then (a, b) =

• A. (0, – 4)
• B. (0, 4)
• C. (4, 0)
• D. (– 4, 0)

Answer 1

Answer: (C)

(4, 0)

Answer 2

Third vertex

$\left( \frac{x_{1} + x_{2} \pm \sqrt{3}(y_{2}–y_{1})}{2},\frac{y_{1} + y_{2} \mp \sqrt{3}(x_{2}–x_{1})}{2} \right)$

=$\left( \frac{0 + 2 \pm \sqrt{3}(2\sqrt{3}–0)}{2},\frac{0 + 2\sqrt{3} \mp \sqrt{3}(2–0)}{2} \right)$

= $\left( \frac{2 \pm 6}{2},\frac{2\sqrt{3} \mp 2\sqrt{3}}{2} \right)$

= $\left( \frac{2 + 6}{2},\frac{2\sqrt{3}–2\sqrt{3}}{2} \right)$ or $\left( \frac{2–6}{2},\frac{2\sqrt{3} + 2\sqrt{3}}{2} \right)$

= (4, 0) or (–2, 2$\sqrt{3}$)