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, 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 (−5, 7) and (−3, 3) left parenthesis negative 5 comma 7 right parenthesis and left parenthesis negative 3 comma 3 right parenthesis (−7, 4) and (−5, 0)

Answer 1

To translate a line segment to the left and down, you will subtract from the x-coordinates for leftward movement and subtract from the y-coordinates for downward movement.

1. Original endpoints:

   • Point A: (-2, 7)
   • Point B: (0, 3)

2. Translation:

   • Translate 3 units to the left:

     • For Point A: \(-2 - 3 = -5\)
     • For Point B: \(0 - 3 = -3\)

   • Translate 5 units down:

     • For Point A: \(7 - 5 = 2\)
     • For Point B: \(3 - 5 = -2\)

3. New endpoints after translation:

   • Translated Point A: (-5, 2)
   • Translated Point B: (-3, -2)

So the new endpoints after translating the line segment are (−5, 2) and (−3, −2), which corresponds to the first option in your responses.