How does the order matter when making rules for translations, rotations, reflections and dilations?
Select the point (neither the x-value or y-value my be 0).
Write down two different types of rules and preform them in order. What is your final point?
Use the same original point and the same two rules but switch order. What is your final point
Show all of your steps.
The order in which rules are applied for translations, rotations, reflections, and dilations can affect the final result.
For translations, the order of rules does not matter. The result will be the same no matter which order the translations are performed.
For rotations, reflections, and dilations, the order of rules does matter.
Let's take the point (3,2) as our original point.
First, let's perform two different types of rules in order: translation followed by rotation.
Translation rule (x+1, y-3) results in the new point (3+1, 2-3) = (4, -1).
Rotation rule of 90 degrees counterclockwise rotates the point (-1, 4) to (-4, -1).
So, the final point after performing translation and rotation in order is (-4, -1).
Now, let's switch the order of the same two rules: rotation followed by translation.
Rotation rule of 90 degrees counterclockwise rotates the point (3,2) to (-2, 3).
Translation rule (-2+1, 3-3) results in the new point (-1, 0).
So, the final point after performing rotation and translation in order is (-1, 0).
In summary:
- Performing translation followed by rotation: Final point (-4, -1)
- Performing rotation followed by translation: Final point (-1, 0)