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February 28th, 2018, 06:23 AM   #1
Joined: Feb 2018
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Calculate third point from 2 points and an angle

I'm having a hard time putting together a formula. I have 2 points (x0, y0) and (x1, y1) and an angle (k).
Using this information I need to calculate a third point that is k degrees from the previous 2 points.
The problem is something like this:

Is it possible to do that? Thank you for your attention.

Last edited by skipjack; February 28th, 2018 at 08:20 AM.
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February 28th, 2018, 08:41 AM   #2
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Do you require the two lines shown in the diagram to be the same length?

If so, call that length r. The point C will then be (r*cos(θ), r*sin(θ)),
where r = √((x1 - x0)² + (y1 - y0)²) and the angle θ is chosen appropriately.

Do you see how to choose θ?

Note that this is essentially a trigonometry question, so I've moved the thread to the trigonometry forum. If the point C is obtained by a rotation, as suggested above, its coordinates are given by a standard formula that is mathematically equivalent to what I referred to above, but has a more elegant form, especially if described by use of a rotation matrix.
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