Question

kyla applied $r_m cdot t_{0,3}$ 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.

Explanation:

Step1: Analyze the transformation notation

The notation $r_m\cdot T_{0,3}$ means a reflection $r_m$ followed by a translation $T_{0,3}$.

Step2: Check each option

• Option 1: She applied the rotation to the triangle first. The notation doesn't indicate rotation, so this is incorrect.
• Option 2: She applied the reflection to the triangle first. According to the notation, reflection should be first, this is correct.
• Option 3: The triangle has changed in size. A translation $T_{0,3}$ is a rigid - motion and should not change size. Since the size has changed, this is a mistake.
• Option 4: She translated the triangle down instead of just applying a reflection. The notation has both reflection and translation, but the translation is not done correctly as there is a size - change issue, and this option is not relevant to the main mistakes.
• Option 5: She applied a rotation instead of a reflection. The notation indicates reflection, not rotation, so this is incorrect.

Answer:

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