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

(−7, 4) and (−5, 0)

(1, 2) and (3,−2)

(−5, 2) and (−3,−2)

(−5, 7) and (−3, 3)

Answer 1

To translate the endpoints of the line segment 3 units to the left and 5 units down, we need to adjust the coordinates of each endpoint accordingly.

• Translating 3 units to the left means we subtract 3 from the x-coordinate.
• Translating 5 units down means we subtract 5 from the y-coordinate.

Now, let's apply these translations to the endpoints of the line segment:

1. For the first endpoint \((-2, 7)\):

   • New x-coordinate: \(-2 - 3 = -5\)
   • New y-coordinate: \(7 - 5 = 2\)
   • So the new coordinates are \((-5, 2)\).

2. For the second endpoint \((0, 3)\):

   • New x-coordinate: \(0 - 3 = -3\)
   • New y-coordinate: \(3 - 5 = -2\)
   • So the new coordinates are \((-3, -2)\).

Putting this all together, the translated endpoints are \((-5, 2)\) and \((-3, -2)\).

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