Question

Translations and reflections quick check
Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are -2,7 and 0,3

Answer 1

To translate a line segment, you move each endpoint by the given amounts in the specified directions. For this translation, we will move each endpoint 3 units to the left and 5 units down.

1. **Starting points:**

- Endpoint A: (-2, 7)
- Endpoint B: (0, 3)

2. **Translation Vector:**
- Move 3 units to the left means subtracting 3 from the x-coordinate.
- Move 5 units down means subtracting 5 from the y-coordinate.

3. **Calculating the new endpoints:**

- For Endpoint A (-2, 7):
- New x-coordinate: \(-2 - 3 = -5\)
- New y-coordinate: \(7 - 5 = 2\)
- New Endpoint A: \((-5, 2)\)

- For Endpoint B (0, 3):
- New x-coordinate: \(0 - 3 = -3\)
- New y-coordinate: \(3 - 5 = -2\)
- New Endpoint B: \((-3, -2)\)

4. **Result:**
The new endpoints after the translation are:
- New Endpoint A: \((-5, 2)\)
- New Endpoint B: \((-3, -2)\)

Thus, the line segment with endpoints (-2, 7) and (0, 3), after being translated 3 units to the left and 5 units down, has new endpoints at (-5, 2) and (-3, -2).