Question

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

• A. An equilateral triangle
• B. An isosceles triangle
• C. A right angled triangle
• D. None of these

Answer 1

Answer: (B)

An isosceles triangle

Answer 2

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

Then $A B ^ { 2 } = \left( \frac { a } { \sqrt { 3 } } - \frac { 2 a } { \sqrt { 3 } } \right) ^ { 2 } + ( a - 2 a ) ^ { 2 } = \frac { a ^ { 2 } } { 3 } + a ^ { 2 } = \frac { 4 a ^ { 2 } } { 3 }$

Similarly $B C ^ { 2 } = \frac { 4 a ^ { 2 } } { 3 }$ and $A C ^ { 2 } = 4 a ^ { 2 }$

Hence it is an isosceles triangle.