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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

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

(−5, 7)
and (−3, 3)

1 answer

To translate a line segment, we need to apply the translation to both endpoints. The translation specified is 3 units to the left (which decreases the x-coordinate by 3) and 5 units down (which decreases the y-coordinate by 5).

Given the endpoints of the line segment:

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

Translating the first endpoint \((-2, 7)\):

  • Move 3 units to the left: \[ -2 - 3 = -5 \]
  • Move 5 units down: \[ 7 - 5 = 2 \]

So, the new coordinates for the first endpoint become \((-5, 2)\).

Translating the second endpoint \((0, 3)\):

  • Move 3 units to the left: \[ 0 - 3 = -3 \]
  • Move 5 units down: \[ 3 - 5 = -2 \]

So, the new coordinates for the second endpoint become \((-3, -2)\).

Final Translated Endpoints:

  • The translated endpoints are \((-5, 2)\) and \((-3, -2)\).

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