Perform the transformations in different orders and check when we end at the treasure.
Example Solution:
Rotate by 180^(∘) about the origin.
Rotate by 90^(∘) counterclockwise about the origin.
Reflect in the y-axis.
Translate 1 unit right and 1 unit up.
Practice makes perfect
Let's take a look at the given diagram.
It shows a green point ( ∙) and a red X ( *) on the coordinate plane. The ( ∙) is our position and the ( *) is the position of the treasure. We can find this treasure by performing the following four transformations in a correct order.
These transformations are not in the correct order but let's assign each of them a number. Then we can call each transformation by its number without writing down the whole transformation.
Rotate 180^(∘) about the origin.
Reflect in the y-axis.
Rotate 90^(∘) counterclockwise about the origin.
Translate 1 unit right and 1 unit up.
Now, let's try to use our transformations to move the ( ∙) to the ( *).
When we tried enough combinations, we found that the following order works!
Number
Transformation
1.
Rotate 180^(∘) about the origin.
3.
Rotate 90^(∘) counterclockwise about the origin.
2.
Rotate in the y-axis.
4.
Translate 1 unit right and 1 unit up.
However, it is not the only solution. We can see some other orders that allow us to find the treasure!
1 → 3 → 2 → 4 [0.5em]
3 → 1 → 2 → 4 [0.5em]
1 → 4 → 3 → 2 [0.5em]
3 → 2 → 1 → 4
We can check that this is the case.
