Any 90^(∘) rotation about the origin will change a horizontal rectangle into a vertical rectangle.
See solution.
Practice makes perfect
We want to describe two different sequences of transformations that move the red figure onto the blue one. The two figures are rectangles. They have the same shape, but they are placed differently.
The red rectangle is horizontal and the blue one is vertical. To map the red rectangle onto the blue one, we should use a transformation that changes a horizontal rectangle into a vertical one. A 90^(∘) rotation about the origin in either direction will work here.
Transformation
Effect
Rotation by 90^(∘) clockwise about the origin.
( x, y) ↓ ( y, - x)
Rotation by 90^(∘) counterclockwise about the origin.
( x, y) ↓ ( - y, x)
Let's see how the red rectangle changes after applying either of these transformations.
The red rectangle is also vertical after either of these rotations. Next, we can translate the red rectangle until it matches the blue one.
Now, we have two sequences of transformations that map the red figure onto the blue one. Let's list them!
Rotation
Translation
First Sequence
Rotate by 90^(∘) clockwise about the origin.
Translate by 1 unit right and 5 units up.
Second Sequence
Rotate by 90^(∘) counterclockwise about the origin.
