The points 0-0-a- 0 and a-2- a -3-2 are vertices ofA- Isosceles triangleB- Equilateral triangleC- Scalene triangleD- None of these

The correct option is B Equilateral triangle Let A(0, 0), B(a, 0) and C (a/2, a√(3)/2) Hence AB = √(a^2 + 0) = a, BC = √(( a/2)^2 + ( a√(3)/2)^2) = a and AC = ...

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Byju's Answer

Standard XII

Mathematics

Family of Straight Lines

The points 0,...

Question

The points (0, 0), (a, 0) and $(\frac{a}{2}, \frac{a \sqrt{3}}{2})$ are vertices of

Isosceles triangle

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Equilateral triangle

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Scalene triangle

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None of these

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Solution

The correct option is B
Equilateral triangle

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

Hence AB = $\sqrt{a^{2} + 0}$ = a, BC = $\sqrt{{(\frac{a}{2})}^{2} + {(\frac{a \sqrt{3}}{2})}^{2}}$ = a

and AC = $\sqrt{{(\frac{a}{2})}^{2} + {(\frac{a \sqrt{3}}{2})}^{2}}$ = a

Hence the triangle is equilateral.

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