How to rotate a line around one of its vertexes

Question

I am making my first raycasting engine, and would like to rotate a line over an angle θ

How does one do this? Would it be possible to show me some basic C++ code or some pseudocode?

This image describes my problem:

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Optional question

I decided to make all of this in graphics.h, because it is the simplest graphics header for C/C++.

Answer 1

You want:

B = P + M * (A - P)

Where M is a 2D rotation matrix:

M = |  cos(ϴ)  -sin(ϴ) |
    |  sin(ϴ)   cos(ϴ) |

In C++ it could be written as:

float c = cos(theta), s = sin(theta);
float dx = ax - px, dy = ay - py;
float bx = px + c * dx - s * dy;
float by = py + s * dx + c * dy;