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 (−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)

Answer 1

To translate a line segment, we move each endpoint by a given set of directions. In this case, we are translating the line segment 3 units to the left and 5 units down.

The transformation can be done using the following formulas:
- For a translation 3 units to the left, we subtract 3 from the x-coordinate.
- For a translation 5 units down, we subtract 5 from the y-coordinate.

Now let's apply these transformations to each endpoint of the line segment.

1. For the first endpoint \((-2, 7)\):
- New x-coordinate: \(-2 - 3 = -5\)
- New y-coordinate: \(7 - 5 = 2\)
- Translated point: \((-5, 2)\)

2. For the second endpoint \((0, 3)\):
- New x-coordinate: \(0 - 3 = -3\)
- New y-coordinate: \(3 - 5 = -2\)
- Translated point: \((-3, -2)\)

Therefore, the new coordinates of the endpoints after the translation are \((-5, 2)\) and \((-3, -2)\).

The correct response is:
\((−5, 2)\) and \((−3,−2)\)