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

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

(1, 2)
and (3,−2)
left parenthesis 1 comma 2 right parenthesis and left parenthesis 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

Answer 1

To translate a line segment, you need to move both endpoints by the same amount in the specified directions.

For your line segment with endpoints \((-2, 7)\) and \((0, 3)\):

1. **Translate 3 units to the left:**
- For the point \((-2, 7)\):
\[
-2 - 3 = -5 \quad \text{(x-coordinate)}
\]
So, the new point is \((-5, 7)\).

- For the point \((0, 3)\):
\[
0 - 3 = -3 \quad \text{(x-coordinate)}
\]
So, the new point is \((-3, 3)\).

2. **Translate 5 units down:**
- For the new point \((-5, 7)\):
\[
7 - 5 = 2 \quad \text{(y-coordinate)}
\]
So, the new point is \((-5, 2)\).

- For the new point \((-3, 3)\):
\[
3 - 5 = -2 \quad \text{(y-coordinate)}
\]
So, the new point is \((-3, -2)\).

Combining the results, the new endpoints after the translation are \((-5, 2)\) and \((-3, -2)\).

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