A line segment has endpoints (2,−1)

Question

and (5, −4)
. What are the new endpoints after rotating the segment 90°
clockwise?(1 point)
Responses

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

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

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

(−2, 1)
and (−5, 4)

Answer 1

To rotate a point \( (x, y) \) 90° clockwise about the origin, the new coordinates are given by \( (y, -x) \).

Let's apply this transformation to the endpoints of the line segment: \( (2, -1) \) and \( (5, -4) \).

1. Rotate \( (2, -1) \):

   • New coordinates: \( (-1, -2) \)

2. Rotate \( (5, -4) \):

   • New coordinates: \( (-4, -5) \)

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

The correct response is:

(−1, −2) and (−4, −5).