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

(−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)

Answer 1

To find the new endpoints after rotating the segment 90° clockwise, we can follow these steps:

1. Identify the original endpoints of the line segment: \( A(2, -1) \) and \( B(5, -4) \).

2. To rotate a point \( (x, y) \) 90° clockwise around the origin, we can use the transformation: \[ (x, y) \to (y, -x) \]

3. Apply this transformation to each endpoint:

   • For point \( A(2, -1) \): \[ (2, -1) \to (-1, -2) \]

   • For point \( B(5, -4) \): \[ (5, -4) \to (-4, -5) \]

4. Therefore, the new endpoints after a 90° clockwise rotation are:

   • \( A'(-1, -2) \)
   • \( B'(-4, -5) \)

So, the correct answer is: (−1, −2) and (−4, −5).