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

(−7, 4)
and (−5, 0)
left parenthesis negative 7 comma 4 right parenthesis and left parenthesis negative 5 comma 0 right parenthesis

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

(−5, 2)
and (−3,−2)

Answer 1

To demonstrate the translation of a line segment by 3 units to the left and 5 units down, we'll take the original endpoints of the line segment \((-2, 7)\) and \((0, 3)\) and apply the translation.

**Translation rules:**
- Moving 3 units to the left means we subtract 3 from the x-coordinates.
- Moving 5 units down means we subtract 5 from the y-coordinates.

Now, let's apply these translations to the endpoints:

1. For the first endpoint \((-2, 7)\):
- New x-coordinate: \(-2 - 3 = -5\)
- New y-coordinate: \(7 - 5 = 2\)
- So, the new point is \((-5, 2)\).

2. For the second endpoint \((0, 3)\):
- New x-coordinate: \(0 - 3 = -3\)
- New y-coordinate: \(3 - 5 = -2\)
- So, the new point is \((-3, -2)\).

Thus, after translating the line segment, the new endpoints are:

\((-5, 2)\) and \((-3, -2)\).

Therefore, the correct response is:
**\((-5, 2)\) and \((-3, -2)\)**.