Exercise 5 Page 65

We want to describe a sequence of rigid motions between the given figures.

Notice that the figures are in different quadrants. We can start by applying a

9 0^{\circ}

clockwise rotation to match the quadrant of the red figure.

Now, we need to translate the blue figure

4

units to the right.

Finally, let's translate the blue figure

1

unit down.

The sequence of rigid motions between the figures is a rotation of

9 0^{\circ}

clockwise and a translation of

4

units to the right and

1

unit down. Note that we have only shown one of many possible equivalent examples.

Alternative Solution

Another Example

Let's now consider another way to solve this exercise. We can find another sequence of rigid motions between the figures by applying transformations on the red figure. We will start by translating the red figure

4

units to the left.

Now, we will rotate the red figure

9 0^{\circ}

counterclockwise.

The two figures are in the same quadrant. Finally, we will move the red figure

1

unit to the left to get the blue figure.

Therefore, the sequence of rigid motions between the figures is

4

units to the left and a rotation of

9 0^{\circ}

counterclockwise, followed by a translation of

1

unit to the left.