# Polar coordinates

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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)

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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#2

(Original post by

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)

**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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(Original post by

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?

**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?

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#4

(Original post by

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?

**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?

__equilatera__l, the angle (at the centre) between any two vertices will be...?

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