##### Exercise2

This exercise investigates the composition of reflections in the plane.

1. Find the result of first reflecting in the line $$y=0$$ and then $$y=x\text{.}$$ What familiar operation is the cumulative effect of this composition?

2. What happens if you compose the operations in the opposite order; that is, what happens if you first reflect in $$y=x$$ and then $$y=0\text{?}$$ What familiar operation results?

3. What familiar geometric operation results if you first reflect in the line $$y=x$$ and then $$y=-x\text{?}$$

4. What familiar geometric operation results if you first rotate by $$90^\circ$$ and then reflect in the line $$y=x\text{?}$$

It is a general fact that the composition of two reflections results in a rotation through twice the angle from the first line of reflection to the second. We will investigate this more generally in Exercise 8

in-context