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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
The points $\left( {\frac{a}{{\sqrt 3 }},a} \right),\;\left( {\frac{{2a}}{{\sqrt 3 }},\,2a} \right),\;\left( {\frac{a}{{\sqrt 3 }},\,3a} \right)$ are the vertices of
  • A
    An equilateral triangle
  • ✓
    An isosceles triangle
  • C
    A right angled triangle
  • D
    None of these
✓

Answer

Correct option: B.
An isosceles triangle
b
(b) Let $A\,\left( {\frac{a}{{\sqrt 3 }},\,a} \right),\,\,B\,\left( {\frac{{2a}}{{\sqrt 3 }},\,\,2a} \right)$ and $C\,\left( {\frac{a}{{\sqrt 3 }},\,\,3a} \right)$

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

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

Hence it is an isosceles triangle.

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