adityad
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#1
Report Thread starter 6 months ago
#1
Okay so the question is
One vertex of an equilateral triangle has polar coordinates A(4, pi/4). Find the polar coordinates of all the other possible vertices B and C of the triangle, when:
(i) The origin O is at the centre of the triangle
(ii) B is the origin
(iii) O is the midpoint of one of the sides of the triangle

I'm stuck at (i). I'm not sure how to go about doing this - I guess this is more of a geometry question than a polar coordinates question.
The anwsers in the mark scheme for (i) and (ii) are:
(i) B(4, -5pi/12) C(4, 11pi/12)
(ii) B(0, 0) and C either (4, - pi/12) or (4, 7pi/12)
Last edited by adityad; 6 months ago
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ghostwalker
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#2
Report 6 months ago
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(Original post by adityad)
Okay so the question is
One vertex of an equilateral triangle has polar coordinates A(4, pi/4). Find the polar coordinates of all the other possible vertices B and C of the triangle, when:
(i) The origin O is at the centre of the triangle
(ii) B is the origin
(iii) O is the midpoint of one of the sides of the triangle

I'm stuck at (i). I'm not sure how to go about doing this - I guess this is more of a geometry question than a polar coordinates question.
The anwsers in the mark scheme for (i) and (ii) are:
(i) B(4, -5pi/12) C(4, 11pi/12)
(ii) B(0, 0) and C either (4, - pi/12) or (4, 7pi/12)

Looks like they mean the circumcentre when they refer to the centre. This is a point equidistant from all vertices. You then need to exploit the fact that the triangle is equilateral - i.e has rotational symmetry.

Can you take it from there?
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adityad
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#3
Report Thread starter 6 months ago
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(Original post by ghostwalker)
Looks like they mean the circumcentre when they refer to the centre. This is a point equidistant from all vertices. You then need to exploit the fact that the triangle is equilateral - i.e has rotational symmetry.

Can you take it from there?
I tried to sketch but nothing seems to be working. I don't get how rotational symmetry plays into this. Can you give me any more clues?
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ghostwalker
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#4
Report 6 months ago
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(Original post by adityad)
I tried to sketch but nothing seems to be working. I don't get how rotational symmetry plays into this. Can you give me any more clues?
Since O is the centre and the triangle is equilateral, the angle (at the centre) between any two vertices will be...?
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