Question

For today's homework, you will need to recreate the teacher's work on a triangle transformation. Choose the correct way to find the transformations. Select all that apply. (Hint: It is a rigid transformation.)

A. Translate by 〈2, 4〉, then reflect over the line x = 3.
B. Translate by 〈2, 4〉 then reflect over the line x = 5.
C. Rotate 180° about (4, 2), then reflect over the line y = 5.
D. Reflect triangle ABC over the line x = 3 then translate by 〈2, 4〉.

Answer 1

Based on the analysis, the correct ways to find the transformations are options A and D. These options involve combinations of translations and reflections, which are rigid transformations.

Step-by-step explanation:

To find the correct way to transform the triangle, we need to consider rigid transformations, which include translations, rotations, and reflections.

Let's analyze each option:

A. Translate by 〈2, 4〉, then reflect over the line x = 3.

• This option includes a translation and a reflection. Both are rigid transformations, so it could be a correct choice.

B. Translate by 〈2, 4〉 then reflect over the line x = 5.

• This option includes a translation and a reflection. However, the reflection is over the line x = 5, not x = 3. Therefore, this option is incorrect.

C. Rotate 180° about (4, 2), then reflect over the line y = 5.

• This option includes a rotation and a reflection. Although a rotation is a rigid transformation, it is not mentioned that the triangle needs to be rotated. Therefore, this option is incorrect.

D. Reflect triangle ABC over the line x = 3 then translate by 〈2, 4〉.

• This option includes a reflection and a translation. Both are rigid transformations, so it could be a correct choice.

Based on the analysis, the correct ways to find the transformations are options A and D. These options involve combinations of translations and reflections, which are rigid transformations.