To translate the line segment with endpoints (0, 0) and (5, 4) up 3 units and left 2 units, we perform the following operations on each endpoint:
- Translate up 3 units: This means we add 3 to the y-coordinate.
- Translate left 2 units: This means we subtract 2 from the x-coordinate.
Now we apply these translations to each endpoint.
For the endpoint (0, 0):
- New x-coordinate: \(0 - 2 = -2\)
- New y-coordinate: \(0 + 3 = 3\)
New endpoint: \((-2, 3)\).
For the endpoint (5, 4):
- New x-coordinate: \(5 - 2 = 3\)
- New y-coordinate: \(4 + 3 = 7\)
New endpoint: \((3, 7)\).
Therefore, the new endpoints are:
- The new endpoint for (0, 0) is: (-2, 3).
- The new endpoint for (5, 4) is: (3, 7).