Question
when I use the line segments to connect the corresponding points of a pre-image and the image in a translations, the line segments are _______ and _______ because?
Answers
GPT-4o mini
When you use line segments to connect the corresponding points of a pre-image and its image in a translation, the line segments are **congruent** and **parallel** because:
1. **Congruent**: The lengths of the line segments connecting corresponding points in the pre-image and the image are equal. This is true because a translation moves each point the same distance in a specified direction, so the distance between corresponding points remains constant.
2. **Parallel**: The line segments are parallel to each other because all points are moved in the same direction by the same distance. Hence, if you draw line segments connecting corresponding points, those segments will run in the same direction as the translation vector, making them parallel.
In summary, the line segments are congruent because they are the same length after the translation, and they are parallel because they have the same direction as the movement of the translation.
1. **Congruent**: The lengths of the line segments connecting corresponding points in the pre-image and the image are equal. This is true because a translation moves each point the same distance in a specified direction, so the distance between corresponding points remains constant.
2. **Parallel**: The line segments are parallel to each other because all points are moved in the same direction by the same distance. Hence, if you draw line segments connecting corresponding points, those segments will run in the same direction as the translation vector, making them parallel.
In summary, the line segments are congruent because they are the same length after the translation, and they are parallel because they have the same direction as the movement of the translation.