# MATLAB: Need help with matrix manipulati​on/transfo​rmation to reflect points about an axis

MATLABmatrix manipulation

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.

Solved problem by first doing a coordinate transformation and then mirroting across the new y-axis.
z=[cos(theta) sin(theta);-sin(theta) cos(theta)]; % Calculate transformation matrix
m=[x;y]; % Combine x & y coordinates in a single matrix
k=z*m; % Multiply matrices to get x & y values wrt new coordinate system
x_new=k(1,:);
y_new=k(2,:);
mirrored_x=-fliplr(x_new);
mirrored_y=fliplr(y_new);