How does the order matter when making rules for translations, rotations, reflections and dilations?
Select a point (neither the x-value or y-value may be 0).
Write down two different types of rules (translations, rotations, reflections and dilations) and perform them in one order. What is your final point?
Use the same original point and the same two rules but switch the order. What is your final point?
Show all of your steps.
Math
The order does matter when making rules for translations, rotations, reflections, and dilations. Each of these transformations has specific rules and formulas that dictate how they should be applied to a point or an object. Changing the order in which these transformations are performed can result in different outcomes.
For example, let's consider a point (2, 3) as our original point.
Translation:
Rule 1: Move the point 3 units to the right and 2 units up.
Rule 2: Move the point 1 unit to the left and 4 units down.
Applying Rule 1 first:
(2, 3) + (3, 2) = (5, 5)
Applying Rule 2 second:
(5, 5) + (-1, -4) = (4, 1)
Applying Rule 2 first:
(2, 3) + (-1, -4) = (1, -1)
Applying Rule 1 second:
(1, -1) + (3, 2) = (4, 1)
As you can see, the final points are different depending on the order of the translations. Therefore, the order matters when performing multiple translations.
Similarly, when performing rotations, reflections, and dilations, the order of operations can also affect the final outcome. It is important to follow the correct rules and perform the transformations in the specified order to obtain accurate results.