If a vertex of an equilateral triangle is on origin and seco... | MATH - POINTS RELATE TO TRIANGLE (ORTHOCENTRE,...) | SolveeIt | Solveeit

Today, August 18

Question

If a vertex of an equilateral triangle is on origin and second vertex is (4, 0), then its third vertex is-

A

$(2, \pm \sqrt{3})$

B

$(3, \pm \sqrt{2})$

C

$(2, \pm 2\sqrt{3})$

D

$(3, \pm 2\sqrt{2})$

Answer

$(2, \pm 2\sqrt{3})$

Explanation

Solution

Third vertx

$\left\lbrack \frac{0 + 4 \pm \sqrt{3}(0 - 0)}{2},\frac{0 + 0 \pm \sqrt{3}(4 - 0)}{2} \right\rbrack$

$(2, \pm 2\sqrt{3})$