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

Answer 1

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

\[ (x, y) \rightarrow (y, -x) \]

Now, let's apply this transformation to both endpoints of the line segment:

1. For the first endpoint \( (2, -1) \): \[ (2, -1) \rightarrow (-1, -2) \]

2. For the second endpoint \( (5, -4) \): \[ (5, -4) \rightarrow (-4, -5) \]

Thus, after rotating the segment 90° clockwise, the new endpoints will be:

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

The correct response is:

\((-1, -2)\) and \((-4, -5)\)