How to get coordinates of point knowing distance from x,y without know angle?

Question

Starting from this question How to get coordinates of point knowing distance from x,y and angle? I would to know if there is a method to get the same result but without the knowing of the $\alpha$ angle.

Answer 1

If you're going by the linked question, then no. It's easy to see; remove the angle, and notice that

• you now have infinitely many points satisfying the criterion
• all information about the vector $v$ becomes redundant

You need to know two things to be able to move from one point to another, one is how far it is, which gives you a circle of equidistant points, and the second is the direction which reduces your options to a unique point. The distance is given in the norm and the direction in the angle $\alpha$ and the vector $v$ with respect to which the angle is measured (it is also necessary to know in which direction the angle is measured, but this direction is agreed on due to convention.

You can use other methods to represent the same information; this may be a displacement vector in $x$ and $y$, a dot product of some sort, but the information carried is essentially the same.