Question

show that the points (2,2),(-2,-2) and (-2root3,2 root3) are the vertices of an equilateral triangle.

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Answer 1

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ANSWER

Let points be ,

z

1

=2+2i , z

2

=−2−2i , z

3

=−2

3

+2

3

i

For equilateral triangle,

By rotation concept,

z

1

−z

3

z

1

−z

2

=e

3

iπ

........... ....... ........ (1)

So,

⟹

2+2i+2

3

−2

3

i

2+2i+2+2i

⟹

(1+

3

)+(1−

3

)i

2+2i

⟹

(1/2+

3

/2)−(−1/2+

3

/2)i

1+i

⟹

e

12

−iπ

e

4

iπ

⟹e

3

π

So, eq. (1) , satisfies.

Hence, given points are the vertices of an equilateral triangle.

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