How to find the coordinates of a point?

Question

Mathematics

Given a segment and given its coordinates X1,Y1,0 - and its length how to find the coordinates X2,Y2,0?
angle 90, 0 is Z. This problem is for the plane.
My task arose in a right-angled triangle, where the coordinates of the vertices are known, and the straight line I'm talking about is one of the legs
. Just to clarify, the lengths of the second leg are also known, and, accordingly, the hypotenuse. And the coordinates of the leg are known (where the angle is 90 - at the base) and the coordinates of the hypotenuse are known (which are at the base). I need the coordinates of the second leg (which are against the base - on the same line that forms 90).

Answer 1

I misunderstood what needs to be done. But I'll try.
1. Convert the known leg into a vector: (X3−X1, Y3−Y1).
2. Rotate it 90° in the desired direction. For example, x'=y, y'=−x.
3. Bring to the desired length (Pythagorean theorem). The result is a vector leg.
4. Adding a leg vector to the vertex (X1, Y1), we get the second end.