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

(−5, 7)
and (−3, 3)
left parenthesis negative 5 comma 7 right parenthesis and left parenthesis negative 3 comma 3 right parenthesis

(−7, 4)
and (−5, 0)

Answer 1

To translate a line segment, you need to shift each endpoint by the same amount in the specified directions. Here, we want to translate the endpoints of the line segment 3 units to the left and 5 units down.

1. **Starting endpoints:**
- Point A: \((-2, 7)\)
- Point B: \((0, 3)\)

2. **Translation:**
- To translate 3 units to the left, subtract 3 from the x-coordinate of each endpoint.
- To translate 5 units down, subtract 5 from the y-coordinate of each endpoint.

3. **Calculating the new coordinates:**
- For Point A:
\[
\text{New A} = (-2 - 3, 7 - 5) = (-5, 2)
\]
- For Point B:
\[
\text{New B} = (0 - 3, 3 - 5) = (-3, -2)
\]

Thus, the new coordinates after the translation are:
- New Point A: \((-5, 2)\)
- New Point B: \((-3, -2)\)

Therefore, the correct response is:
\[
\text{(−5, 2) and (−3,−2)}
\]