##### Exercise2

This exercise investigates the composition of reflections in the plane.

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?

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?

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

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