MCQ
The points $(0,{\rm{ }}0),\;(a,{\rm{ }}0)$ and $\left( {\frac{a}{2},\,\frac{{a\sqrt 3 }}{2}} \right)$ are vertices of
- AIsosceles triangle
- ✓Equilateral triangle
- CScalene triangle
- DNone of these
✓
Answer
Correct option: B.
Equilateral triangle
b
(b) Let $A\,(0,\,0),\,B\,(a,\,\,0)$ and $C\,\left( {\frac{a}{2},\,\frac{{a\sqrt 3 }}{2}} \right)$
(b) Let $A\,(0,\,0),\,B\,(a,\,\,0)$ and $C\,\left( {\frac{a}{2},\,\frac{{a\sqrt 3 }}{2}} \right)$
Hence $AB = \sqrt {{a^2} + 0} = a,\,\,BC = \sqrt {{{\left( {\frac{a}{2}} \right)}^2} + {{\left( {\frac{{a\sqrt 3 }}{2}} \right)}^2}} = a$
and $AC = \sqrt {{{\left( {\frac{a}{2}} \right)}^2} + {{\left( {\frac{{a\sqrt 3 }}{2}} \right)}^2}} = a$
Hence the triangle is equilateral.
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