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

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

Answer 1

To rotate a point \((x, y)\) 90° clockwise around the origin, the new coordinates become \((y, -x)\).

Let's apply this to each endpoint of the line segment.

1. Rotating the first endpoint (2, -1): \[ (x, y) = (2, -1) \quad \Rightarrow \quad (y, -x) = (-1, -2) \]

2. Rotating the second endpoint (5, -4): \[ (x, y) = (5, -4) \quad \Rightarrow \quad (y, -x) = (-4, -5) \]

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

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