Question

A line segment has endpoints (2,−1)
(
2
,
−
1
)
and (5, −4)
(
5
,

−
4
)
. What are the new endpoints after rotating the segment 90°
90
°
clockwise?(1 point)
Responses

(−1, −2)
(
−
1
,

−
2
)
and (−4, −5)
(
−
4
,

−
5
)
left parenthesis negative 1 comma negative 2 right parenthesis and left parenthesis negative 4 comma negative 5 right parenthesis

(−2, −1)
(
−
2
,

−
1
)
and (−5, −4)
(
−
5
,

−
4
)
left parenthesis negative 2 comma negative 1 right parenthesis and left parenthesis negative 5 comma negative 4 right parenthesis

(−2, 1)
(
−
2
,

1
)
and (−5, 4)
(
−
5
,

4
)
left parenthesis negative 2 comma 1 right parenthesis and left parenthesis negative 5 comma 4 right parenthesis

(2, −1)
(
2
,

−
1
)
and (4, 5)
(
4
,

5
)
left parenthesis 2 comma negative 1 right parenthesis and left parenthesis 4 comma 5 right parenthesis

Answer 1

To rotate the line segment with endpoints (2, -1) and (5, -4) 90° clockwise, we can use the rotation transformation formula.

The general rule for rotating a point (x, y) 90° clockwise around the origin is:
\[
(x, y) \to (y, -x)
\]

We'll apply this transformation to both endpoints:

1. For the point (2, -1):
\[
(2, -1) \to (-1, -2)
\]

2. For the point (5, -4):
\[
(5, -4) \to (-4, -5)
\]

Thus, after rotating the segment 90° clockwise, the new endpoints are (-1, -2) and (-4, -5).

The correct response is:
\[
\text{(−1, −2) and (−4, −5)}
\]