Question

The points (a, a) (–a, -a) and $(–\sqrt{3}a,\sqrt{3}a)$ form the vertices of an

• A. Scalene triangle
• B. Right angled triangle
• C. Isosceles Right angled triangle
• D. Equilateral triangle

Answer 1

The correct option is D

Equilateral triangle

Let the points be A(a, a), B(-a, -a), C $(–\sqrt{3}a,\sqrt{3}a)$

Using distance formula,
BC = $\sqrt{(a+\sqrt{3}a{)}^2+(a-\sqrt{3}a{)}^2}$ = $2\sqrt{2}a$
AB = $\sqrt{(a+a{)}^2+(a+a{)}^2}$ = $2\sqrt{2}a$
AC = $\sqrt{(-a+\sqrt{3}a{)}^2+(-a-\sqrt{3}a{)}^2}$ = $2\sqrt{2}a$

We get AB = BC = AC = 2$\sqrt{2}$ a

Therefore ABC is an equilateral triangle