Question

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, we need to apply the translation to both endpoints. The translation specified is 3 units to the left (which decreases the x-coordinate by 3) and 5 units down (which decreases the y-coordinate by 5).

Given the endpoints of the line segment:
1. \( (-2, 7) \)
2. \( (0, 3) \)

### Translating the first endpoint \((-2, 7)\):
- Move 3 units to the left:
\[
-2 - 3 = -5
\]
- Move 5 units down:
\[
7 - 5 = 2
\]

So, the new coordinates for the first endpoint become \((-5, 2)\).

### Translating the second endpoint \((0, 3)\):
- Move 3 units to the left:
\[
0 - 3 = -3
\]
- Move 5 units down:
\[
3 - 5 = -2
\]

So, the new coordinates for the second endpoint become \((-3, -2)\).

### Final Translated Endpoints:
- The translated endpoints are \((-5, 2)\) and \((-3, -2)\).

Thus, the correct answer is:
**(−5, 2) and (−3,−2)**.