Composition of Reflections
How would one find a pair of lines m and n such that r_n ° r_m is the translation that is the given transformation?
a) the translation that maps the origin onto (5,0)
b) rotation of 180 degrees about a point (x_0, y_0)
c) rotation of 40 degrees about origin
d) translation T with T(x,y) = (x+3, y+4)
I understand that this has to do with the two-reflection theorem for rotations and translations, but I can't seem to find any examples so that I can fully understand the concept. I came across these in an old textbook and was wondering if anyone would be able to explain how to do problems like this. I appreciate it!