How to calculate $B(x_1,y_1)$ when $\alpha$ and $A(x_0,y_0)$ are known?

Question

In case one want to calculate $\alpha$ angle between $AB$ vector and $x$ axis, it can calculate $\alpha=arctan2(x_1-x_0,y_1-y_0)$. Thus, for example for $A(0,0)$ and $B(10,10)$ one will get $\alpha$ equal to 45°. Is there a way to calculate $x_1,y_1$ coordinates when $\alpha$ angle and $x_0,y_0$ are given?

Answer 1

If we know the distance $AB=r$ than we have: $$ x_1=x_0+r\cos \alpha \qquad y_1=y_0+r \sin \alpha $$