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

(−5, 7)
(
−
5
,

7
)
and (−3, 3)
(
−
3
,

3
)
left parenthesis negative 5 comma 7 right parenthesis and left parenthesis negative 3 comma 3 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

(−7, 4)
(
−
7
,

4
)
and (−5, 0)

Answer 1

To translate a line segment, we need to shift both endpoints horizontally and vertically according to the specified amounts. In this case, we need to translate the line segment 3 units to the left and 5 units down.

Starting endpoints are:

1. \( (-2, 7) \)
2. \( (0, 3) \)

Now let's apply the translation:

Translation for Point 1: \( (-2, 7) \)

• Move left 3 units: \[ -2 - 3 = -5 \]
• Move down 5 units: \[ 7 - 5 = 2 \]
• New coordinates for Point 1: \[ (-5, 2) \]

Translation for Point 2: \( (0, 3) \)

• Move left 3 units: \[ 0 - 3 = -3 \]
• Move down 5 units: \[ 3 - 5 = -2 \]
• New coordinates for Point 2: \[ (-3, -2) \]

Resulting Translated Points:

The new endpoints of the translated line segment are: \[ (-5, 2) \text{ and } (-3, -2) \]

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