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

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

(−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, you need to shift each endpoint by the same amount in the specified directions. Here, we want to translate the endpoints of the line segment 3 units to the left and 5 units down.

1. Starting endpoints:

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

2. Translation:

   • To translate 3 units to the left, subtract 3 from the x-coordinate of each endpoint.
   • To translate 5 units down, subtract 5 from the y-coordinate of each endpoint.

3. Calculating the new coordinates:

   • For Point A: \[ \text{New A} = (-2 - 3, 7 - 5) = (-5, 2) \]
   • For Point B: \[ \text{New B} = (0 - 3, 3 - 5) = (-3, -2) \]

Thus, the new coordinates after the translation are:

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

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