Example Answer: Rotation of 90^(∘) clockwise and a translation of 4 units to the right and 1 unit down
Practice makes perfect
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 90^(∘) 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 90^(∘) 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 90^(∘) 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 90^(∘) counterclockwise, followed by a translation of 1 unit to the left.
