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

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.

Answer 1

[Mark Evans]

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);

Answer 2

[Mark Evans]

Bump