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)

Question

(
−
2
,

7
)
and (0, 3)
(
0
,

3
)
.(1 point)
Responses

(−7, 4)
(
−
7
,

4
)
and (−5, 0)
(
−
5
,

0
)
left parenthesis negative 7 comma 4 right parenthesis and left parenthesis negative 5 comma 0 right parenthesis

(1, 2)
(
1
,

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

(−5, 2)
(
−
5
,

2
)
and (−3,−2)
(
−
3
,
−
2
)
left parenthesis negative 5 comma 2 right parenthesis and left parenthesis negative 3 comma negative 2 right parenthesis

(−5, 7)
(
−
5
,

7
)
and (−3, 3)

Answer 1

To translate a line segment, we adjust the coordinates of its endpoints based on the specified movements. In this case, we want to translate 3 units to the left and 5 units down.

1. Starting Point 1: \((-2, 7)\)

   • Move 3 units to the left: \(-2 - 3 = -5\)
   • Move 5 units down: \(7 - 5 = 2\)
   • New coordinates: \((-5, 2)\)

2. Starting Point 2: \((0, 3)\)

   • Move 3 units to the left: \(0 - 3 = -3\)
   • Move 5 units down: \(3 - 5 = -2\)
   • New coordinates: \((-3, -2)\)

Thus, the translation of the line segment results in the new endpoints \((-5, 2)\) and \((-3, -2)\).

The answer is:
\((-5, 2)\) and \((-3, -2)\)
(Option: \( (−5, 2) \) and \( (−3,−2) \))