Question

Show that the following points form an equilateral triangle.

$(0,0),(10,0)and(5,5\sqrt{3})$

Answer 1

To form equilateral triangle all three sides must be equal

$A=(0,0),$ $B(10,0),$ $C(5,5\sqrt{3})$

$AB=\sqrt{{10}^2}=\sqrt{100}$

$BC=\sqrt{(5-10{)}^2+(5\sqrt{3}{)}^2}=\sqrt{5^2+(5\sqrt{3}{)}^2}=\sqrt{100}$

$AC=\sqrt{5^2+(5\sqrt{3}{)}^2}=\sqrt{100}$

$AB=BC=AC=10$

Hence, it is a equilateral triangle.