I need some help reflecting/mirroring a set of data points across an arbitrary axis. My points are as follows:

x=[6;12;5;3];

y=[0;-1;-7;11];

and I would like to reflect them about a line that goes from (0,0) to (5,10). The line could be any angle but this will work fine for my example.

Ultimately I may have thousands of points but I just need to understand how to do this so that I can apply the technique on a larger scale.

Can someone help me understand how to do this as I am not much of a linear algebra guy. Thanks in advance.

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