Thread: help with points on a circle

If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?


thanks

As you are seeking a pair of co-ordinates

you could set up a pair of equations in 2 unknowns.

If the circle centre is the origin, then



where the other co-ordinates are known.

Then the area of the triangle between the origin and the 2 points is



and so, your 2nd equation is, using the area of a triangle for which one vertex is the origin



However, a trigonometric solution will be much simpler.

If you label the acute angle between the negative part of the x-axis, the origin and the red dot "A",
your given angle "B",
and the obtuse angle between the positive part of the x-axis and the blue dot "C",
then use the given co-ordinates to calculate the circle radius and the angle "A",
then calculate "C" and use

Originally Posted by Sneaky

If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?


thanks

p-radius(not x, for this matter)

x=pcos (a)
y=psin(a)

you have red point, (x1,y1) put it above, find angle a.

blue point is:

x=pcos (a-b)
y=psin(a-b)

b is your rotation angle.

I think that would work...

Originally Posted by Sneaky

If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?

Let's change some of the notation here. Say that the the coordinates of the red point are then the coordinates of the blue point can be found using:


NOTE. I have changed the notation. is the angle you have called . Also note that you said that you know