Question

The points $(0,\ 0),\mspace{6mu}(a,\ 0)$ and $\left( \frac{a}{2},\frac{a\sqrt{3}}{2} \right)$ are vertices of.

• A. Isosceles triangle
• B. Equilateral triangle
• C. Scalene triangle
• D. None of these

Answer 1

Answer: (B)

Equilateral triangle

Answer 2

Let $A ( 0,0 ) , B ( a , 0 )$ and $C \left( \frac { a } { 2 } , \frac { a \sqrt { 3 } } { 2 } \right)$

Hence $A B = \sqrt { a ^ { 2 } + 0 } = a , B C = \sqrt { \left( \frac { a } { 2 } \right) ^ { 2 } + \left( \frac { a \sqrt { 3 } } { 2 } \right) ^ { 2 } } = a$

And $A C = \sqrt { \left( \frac { a } { 2 } \right) ^ { 2 } + \left( \frac { a \sqrt { 3 } } { 2 } \right) ^ { 2 } } = a$

Hence the triangle is equilateral.