MHB Calculate third point from 2 points and an angle

AI Thread Summary
To calculate a third point from two given points and an angle, the discussion outlines a method for rotating the second point around the first point. The formula provided involves using trigonometric functions to determine the new coordinates based on the specified angle. The calculations for the new point (Cx, Cy) are confirmed to correctly represent the rotation of the second point around the first. This approach effectively allows for determining the position of the third point at the desired angle. The method is validated as accurate for the intended purpose.
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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.
View attachment 7880
Is it possible to do that? Thank you for your attention.
 

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From your diagram, it looks as though the point C is found by rotating (x1,y1) about (x0,y0) by an angle of x degrees. Is this what you want? If so, there are standard ways of doing this problem. If you need further help on this, post again.
 
I found a method:

Cx=cos(θ)⋅(X1−X0)−sin(θ)⋅(Y1−Y0)+X0
Cy=sin(θ)⋅(X1−X0)+cos(θ)⋅(Y1−Y0)+Y1

Is it right?
 
Yes, this rotates (x1,y1) about (x0,y0) through an angle of $\theta$.
 
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