Question

kyla applied $r_{m}circ t_{0,3}$ 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 transformation notation

The notation $r_m\circ T_{0,3}$ means first perform translation $T_{0,3}$ (translation 3 units in the y - direction) and then reflection $r_m$ (reflection over line $m$).

Step2: Check each option

• Option 1: She applied the rotation to the triangle first. Since there is no rotation in $r_m\circ T_{0,3}$, this is not a correct statement.
• Option 2: She applied the reflection first. It should be translation first, so this is a mistake.
• Option 3: $T_{0,3}$ is a translation and there is no indication of a size - change operation in the given transformation, but if the triangle's size is changed, it is a mistake as the given transformation doesn't imply resizing.
• Option 4: The transformation implies translation first and then reflection, not translation instead of reflection, so this is not a correct statement.
• Option 5: The transformation has no rotation, so this is not a correct statement.

Answer:

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