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A line segment has endpoints (2,−1)

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

(−2, −1) and (−5, −4)

(−1, −2) and (−4, −5)

(2, −1) and (4, 5)

(−2, 1) and (−5, 4)

1 answer

To rotate a point \( (x, y) \) 90° clockwise around the origin, you can use the formula:

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

We'll rotate both endpoints of the line segment:

  1. For the endpoint \( (2, -1) \):

    • \( x' = -1 \)
    • \( y' = -2 \)

    So after rotation, the new point is \( (-1, -2) \).

  2. For the endpoint \( (5, -4) \):

    • \( x' = -4 \)
    • \( y' = -5 \)

    So after rotation, the new point is \( (-4, -5) \).

Hence, after rotating the line segment 90° clockwise, the new endpoints are:

\[ (-1, -2) \text{ and } (-4, -5) \]

The correct response is therefore:

(−1, −2) and (−4, −5).