Question

Find the coordinates of the vertices of an equilateral triangle of side $2a$ with one vertex at origin and side along $x$-axis.

• A. $(0,0)(a,0)(0,\sqrt{2}a)$
• B. $(0,a)(2a,0)(0,\sqrt{2}a)$
• C. $(0,0)(2a,0)(0,\sqrt{3}a)$
• D. None

Answer 1

The correct option is C $(0,0)(2a,0)(0,\sqrt{3}a)$

In equilateral $△ABC$, draw $AD\perp BC$

Since $AB=AC\Rightarrow AD$ is median bisector of $BC$

$\therefore BD=DC=a$

Now $AD=\sqrt{(2a{)}^2-a^2}=\sqrt{3}a$

Coordinates are

$A(0,0)$

$B(2a,0)$

$C(0,\sqrt{3}a)$