Question

demonstrate the translation of a line segment of 3 units to left and 5 units down if the endpoints

Answer 1

To demonstrate the translation of a line segment, we can start with the original endpoints of the segment. Let's assume the original endpoints are:

- Point A: \( (x_1, y_1) = (2, 3) \)
- Point B: \( (x_2, y_2) = (5, 7) \)

To translate this line segment 3 units to the left and 5 units down, we need to adjust the coordinates of both endpoints.

### Translation rules:
- Translating left (negative x-direction): Subtract from the x-coordinate.
- Translating down (negative y-direction): Subtract from the y-coordinate.

### Translation process:
1. **Translate Point A**:
\[
A' = (x_1 - 3, y_1 - 5) = (2 - 3, 3 - 5) = (-1, -2)
\]

2. **Translate Point B**:
\[
B' = (x_2 - 3, y_2 - 5) = (5 - 3, 7 - 5) = (2, 2)
\]

### Resulting Endpoints:
After the translation, the new endpoints of the line segment will be:
- Translated Point A: \( A' = (-1, -2) \)
- Translated Point B: \( B' = (2, 2) \)

### Summary:
The original line segment from \( (2, 3) \) to \( (5, 7) \) is translated to a new line segment from \( (-1, -2) \) to \( (2, 2) \).