To translate a line segment to the left by 3 units and down by 5 units, we need to subtract 3 from the x-coordinates of both endpoints and subtract 5 from the y-coordinates of both endpoints.
The given endpoints of the line segment are:
- Point A: \((-2, 7)\)
- Point B: \((0, 3)\)
Now, we'll perform the translation on both points:
For Point A \((-2, 7)\):
- Translate left by 3 units: \(-2 - 3 = -5\)
- Translate down by 5 units: \(7 - 5 = 2\)
So Point A translates to \((-5, 2)\).
For Point B \((0, 3)\):
- Translate left by 3 units: \(0 - 3 = -3\)
- Translate down by 5 units: \(3 - 5 = -2\)
So Point B translates to \((-3, -2)\).
After performing the translations, the new endpoints of the line segment are:
- \((-5, 2)\) and \((-3, -2)\).
Thus, the correct response is: \((-5, 2)\) and \((-3, -2)\).