Question
A triangle is translated 4 units right and then reflected over the x-axis. What is true about the final image?
A
The final image is larger than the original.
B
The final image is congruent to the original triangle.
C
The final image is a different shape.
D
The final image is smaller than the original.
A
The final image is larger than the original.
B
The final image is congruent to the original triangle.
C
The final image is a different shape.
D
The final image is smaller than the original.
Answers
GPT-4o mini
The transformations applied to the triangle are a translation and a reflection. Let's analyze what each of these transformations does:
1. **Translation (4 units right)**: This transformation moves every point of the triangle 4 units to the right. This does not change the size or shape of the triangle; it simply changes its position.
2. **Reflection over the x-axis**: This transformation flips the triangle over the x-axis. Similar to the translation, this does not change the size or shape of the triangle; it only changes its orientation.
Since both transformations maintain the size and shape of the triangle, the final image will be congruent to the original triangle.
Therefore, the correct answer is:
**B. The final image is congruent to the original triangle.**
1. **Translation (4 units right)**: This transformation moves every point of the triangle 4 units to the right. This does not change the size or shape of the triangle; it simply changes its position.
2. **Reflection over the x-axis**: This transformation flips the triangle over the x-axis. Similar to the translation, this does not change the size or shape of the triangle; it only changes its orientation.
Since both transformations maintain the size and shape of the triangle, the final image will be congruent to the original triangle.
Therefore, the correct answer is:
**B. The final image is congruent to the original triangle.**