⌈1 0⌉⌈x⌉=⌈ x⌉
⌊0 1⌋⌊y⌋=⌊y⌋
The above 2x2 matrix reflects a point over the xaxis. (x,y)→(x,y).
Derive a matrix that will reflect a point over the line y=kx.
(In reply to
re: researched solution by Jer)
The following eliminates the trig functions, but still starts out with the Wikipedia formula involving theta, rather than from scratch:
atan(k) has a sine = k/sqrt(1+k^2) and cosine = 1/sqrt(1+k^k).
cos(2*atan(k)) = 1/(1+k^2)  k^2/(1+k^2) = (1k^2)/(1+k^2)
sin(2*atan(k)) = 2*k/(1+k^2)
[cos(2*atan(k)) sin(2*atan(k))]
[sin(2*atan(k)) cos(2*atan(k))]
then becomes
[(1k^2)/(1+k^2) 2*k/(1+k^2)]
[2*k/(1+k^2) (k^21)/(1+k^2)]

Posted by Charlie
on 20150402 08:50:32 