Two T-shaped objects are shown on the grid.
Which transformations or sequence of transformations prove the objects are congruent? Select ALL that are correct.
Responses
Translate Object 1 by –12 units along the x-axis, and then translate it by –4 along the y-axis.
Translate Object 1 by –12 units along the x-axis, and then translate it by –4 along the y-axis.
Translate Object 1 by –4 units along the x-axis, and then translate it by –12 along the y-axis.
Translate Object 1 by –4 units along the x-axis, and then translate it by –12 along the y-axis.
Reflect Object 1 over the y-axis, and then translate it by −14 along the x-axis.
Reflect Object 1 over the y-axis, and then translate it by −14 along the x-axis.
Rotate Object 1 by 180° counterclockwise about the origin, and then translate it by −2 along the x-axis.
Rotate Object 1 by 180° counterclockwise about the origin, and then translate it by −2 along the x-axis.
Rotate Object 1 by 180° clockwise about the origin, and then translate it by −2 along the x-axis.
Rotate Object 1 by 180° clockwise about the origin, and then translate it by −2 along the x-axis.
Reflect Object 1 over the x-axis, and then translate it by –13 along the x-axis.
Reflect Object 1 over the x-axis, and then translate it by –13 along the x-axis.
All of the above.
To determine if two T-shaped objects are congruent, we need to find a sequence of transformations that can be applied to one object to obtain the other object.
Let's analyze each response option:
1. Translate Object 1 by –12 units along the x-axis, and then translate it by –4 along the y-axis.
2. Translate Object 1 by –4 units along the x-axis, and then translate it by –12 along the y-axis.
Both options involve translating Object 1 in different directions, so they do not prove congruence.
3. Reflect Object 1 over the y-axis, and then translate it by −14 along the x-axis.
4. Reflect Object 1 over the y-axis, and then translate it by −14 along the x-axis.
Both options involve reflecting Object 1 and then translating it, so they do not prove congruence.
5. Rotate Object 1 by 180° counterclockwise about the origin, and then translate it by −2 along the x-axis.
6. Rotate Object 1 by 180° clockwise about the origin, and then translate it by −2 along the x-axis.
Both options involve rotating Object 1 and then translating it, so they do not prove congruence.
7. Reflect Object 1 over the x-axis, and then translate it by –13 along the x-axis.
8. Reflect Object 1 over the x-axis, and then translate it by –13 along the x-axis.
Both options involve reflecting Object 1 and then translating it, so they do not prove congruence.
After analyzing all the options, none of them are correct. None of the given transformations or sequences of transformations prove that the objects are congruent.
The correct transformations or sequence of transformations that prove the objects are congruent are:
1. Translate Object 1 by -4 units along the x-axis, and then translate it by -12 along the y-axis.
2. Rotate Object 1 by 180° counterclockwise about the origin, and then translate it by -2 along the x-axis.
3. Reflect Object 1 over the y-axis, and then translate it by -14 along the x-axis.