You can do either a 90^(∘) counterclockwise rotation about the origin or a reflection in the x-axis in order to change the alignment of the red triangle.
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 right triangles. They have the same shape, but they are placed differently.
The red triangle's right angle points to the top-left (↖), while the blue triangle's points to the bottom-left (↙). We should use a transformation that changes this direction to map the red triangle onto the blue one. A 90^(∘) counterclockwise rotation about the origin or a reflection in x-axis will work here.
Transformation
Effect
Rotation by 90^(∘) counterclockwise about the origin.
( x, y) ↓ ( - y, x)
Reflection in the x-axis.
( x, y) ↓ ( x, - y)
Let's see how the red triangle changes after applying either of these transformations.
The red triangle is now aligned correctly. Next, we can translate the red triangle 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!
Change of Alignment
Translation
First Sequence
Rotate by 90^(∘) counterclockwise about the origin.
