Triangle A B C is reflected across the line of reflection m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is doubled in size to form triangle A double-prime B double-prime C double-prime.

Question

Kyla applied rm ◦ T0,3 to triangle ABC. What mistakes did she make? Check all that apply.

She applied the rotation to the triangle first.
She applied the reflection to the triangle first.
She changed the size of the triangle instead of just applying a translation.
She translated the triangle down instead of just applying a reflection.
She applied a rotation instead of a reflection

Answer 1

To analyze Kyla's application of transformations to triangle ABC, we need to break down what was intended and what may have been executed incorrectly based on the notation "rm ◦ T0,3", where "rm" signifies a reflection across line m and "T0,3" indicates a translation.

1. She applied the rotation to the triangle first.

   • This is an incorrect statement based on the description provided. There's no mention of a rotation being part of the transformation she was expected to perform. She should not have applied a rotation at all.

2. She applied the reflection to the triangle first.

   • If she followed the order of "rm ◦ T0,3," this statement would be incorrect. The reflection should occur after the translation, indicating she may have applied it in the wrong order.

3. She changed the size of the triangle instead of just applying a translation.

   • This could be a mistake depending on what the transformations were meant to achieve. The operation described does not include resizing, so if she altered the size of the triangle, this would indeed be a mistake.

4. She translated the triangle down instead of just applying a reflection.

   • If she applied a translation (which was part of the intended transformation) but incorrectly moved it "down" rather than in the direction indicated by T0,3, then this could be seen as a mistake.

5. She applied a rotation instead of a reflection.

   • If she mistakenly performed a rotation instead of the intended reflection, this would be a mistake.

Given these points, the possible mistakes Kyla made are:

• She applied the rotation to the triangle first. (Incorrect)
• She applied the reflection to the triangle first. (Incorrect if she did so out of order)
• She changed the size of the triangle instead of just applying a translation. (Correct if resizing was not intended)
• She translated the triangle down instead of just applying a reflection. (Correct if translation was not executed correctly)
• She applied a rotation instead of a reflection. (Correct if that occurred)

Thus, the mistakes that Kyla likely made may include the following:

• She changed the size of the triangle instead of just applying a translation.
• She translated the triangle down instead of just applying a reflection.
• She applied a rotation instead of a reflection.

If she reflected before translating or incorrectly executed the transformations in any other way, those points would also be applicable.