Let
be the line that makes an angle of
with the positive
-axis, and
be the line that makes an angle of
with the positive
-axis. We sketch the sequence of reflections below, keeping the original orientation of the axes in the background, labelled as
,
. In the sketch, the image of the
-,
-axes after
is labelled as
,
. The reflection
is then applied to the
-,
-axes, resulting in the
-,
-axes.
Math 152 2022 Q18 solution figure
After the reflection about
, we now look at the angle between the axes
and
, this is
(shown in purple). The
- and
-axes are now
off from their original orientation (taking counterclockwise rotation to be positive).