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

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

Answer 1

To find the new endpoints of the line segment after a 90° clockwise rotation, we can use the rotation transformation for points in the Cartesian plane.

The rotation of a point \((x, y)\) by 90° clockwise around the origin is given by the transformation:

\[ (x', y') = (y, -x) \]

Now, we will apply this transformation to each of the endpoints of the line segment:

1. For the point (2, -1): \[ (x', y') = (-1, -2) \]

2. For the point (5, -4): \[ (x', y') = (-4, -5) \]

Thus, the new endpoints after a 90° clockwise rotation are: \[ (-1, -2) \quad \text{and} \quad (-4, -5) \]

So, the correct response is: \[ (-1, -2) \text{ and } (-4, -5) \]