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

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

Answer 1

To translate a line segment, we subtract the translation amounts from the coordinates of the endpoints.

The original endpoints of the line segment are:
- Point A: \((-2, 7)\)
- Point B: \((0, 3)\)

To translate the segment 3 units to the left and 5 units down, we perform the following calculations for each point:

For Point A \((-2, 7)\):
- Move 3 units left: \(-2 - 3 = -5\)
- Move 5 units down: \(7 - 5 = 2\)

So, after translation, Point A becomes \((-5, 2)\).

For Point B \((0, 3)\):
- Move 3 units left: \(0 - 3 = -3\)
- Move 5 units down: \(3 - 5 = -2\)

So, after translation, Point B becomes \((-3, -2)\).

Thus, the new endpoints after the translation are:
\[
(-5, 2) \text{ and } (-3, -2)
\]

The correct response is:
\((-5, 2) \text{ and } (-3, -2)\)