Question

If the points (1,1) (–1,–1) $( - \sqrt{3},\sqrt{3})$ are the vertices of a triangle, then this triangle is.

• A. Equilateral
• B. Right-angled
• C. Isosceles
• D. None of these

Answer 1

Answer: (A)

Equilateral

Answer 2

Given, vertices of triangle are $A ( 1,1 ) , B ( - 1 , - 1 )$ and $C ( - \sqrt { 3 } , \sqrt { 3 } )$

Now, $A B = \sqrt { ( - 1 - 1 ) ^ { 2 } + ( - 1 - 1 ) ^ { 2 } } = \sqrt { 4 + 4 } = \sqrt { 8 }$

$B C = \sqrt { ( - \sqrt { 3 } + 1 ) ^ { 2 } + ( \sqrt { 3 } + 1 ) ^ { 2 } } = \sqrt { 8 }$

$C A = \sqrt { ( 1 + \sqrt { 3 } ) ^ { 2 } + ( 1 - \sqrt { 3 } ) ^ { 2 } } = \sqrt { 8 }$

i.e., $A B = B C = C A$. So, it is an equilateral triangle.