trouble with reflections
I am having a lot of trouble understanding reflections and formulas. These two problems really have me confused. Any sort of guidance would help. Thank you.
1)By explicit comparison of formulas, verify that if R is the reflection across the x-axis and is the counterclockwise rotation about (0, 0) through the angle , then is the reflection across the line L making an angle with the positive x-axis, for any . Thus, every reflection across a line L passing through (0, 0) equals for some angle .
so but what would be the formula for R so I can apply this to
2)Let R be the reflection across the x-axis and let be the counterclockwise rotation about (0,0) through the angle
b) prove: if is any reflection across a line L passing through (0, 0), then
a) i kinda understand this issue of inverses, am I gonna have to actually apply the formula for p theta? again, not sure about what R is.
b) same thing, but what is the difference between R and R_L??
The reflection R across the x-axis is:
R(x,y) = (x,-y).