Question

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).(1 point)Responses (1, 2)and (3,−2)left parenthesis 1 comma 2 right parenthesis and left parenthesis 3 comma negative 2 right parenthesis(−5, 2)and (−3,−2)left parenthesis negative 5 comma 2 right parenthesis and left parenthesis negative 3 comma negative 2 right parenthesis(−7, 4)and (−5, 0)left parenthesis negative 7 comma 4 right parenthesis and left parenthesis negative 5 comma 0 right parenthesis(−5, 7)and (−3, 3)

Answer 1

To translate a line segment with endpoints \( (-2, 7) \) and \( (0, 3) \) by 3 units to the left and 5 units down, we need to apply the following transformations to each endpoint:

1. For translation to the left by 3 units, we subtract 3 from the x-coordinate.
2. For translation down by 5 units, we subtract 5 from the y-coordinate.

Let's calculate the new coordinates for each endpoint:

### For the first endpoint \( (-2, 7) \):
- New x-coordinate: \( -2 - 3 = -5 \)
- New y-coordinate: \( 7 - 5 = 2 \)
- New endpoint: \( (-5, 2) \)

### For the second endpoint \( (0, 3) \):
- New x-coordinate: \( 0 - 3 = -3 \)
- New y-coordinate: \( 3 - 5 = -2 \)
- New endpoint: \( (-3, -2) \)

### Final Result
After translating the line segment, the new endpoints are:
- First endpoint: \( (-5, 2) \)
- Second endpoint: \( (-3, -2) \)

The correct response is:
\((−5, 2)\) and \((−3,−2)\) (which is the first option in your list).