A line segment has endpoints (2,−1)

Question

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)
  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)
  left parenthesis 2 comma negative 1 right parenthesis and  left parenthesis 4 comma 5 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

GPT-4o mini · Answer

To rotate the endpoints $(2, -1)$ and $(5, -4)$ 90° clockwise, we can use the rotation transformation formulas. The formula for rotating a point $(x, y)$ 90° clockwise around the origin is given by: $$ (x', y') = (y, -x) $$ Now we will apply this transformation to both endpoints. 1. For the point $(2, -1)$: - $x' = y = -1$ - $y' = -x = -2$ - So the new coordinates are $(-1, -2)$. 2. For the point $(5, -4)$: - $x' = y = -4$ - $y' = -x = -5$ - So the new coordinates are $(-4, -5)$. Thus, after rotating the segment 90° clockwise, the new endpoints are: $(-1, -2)$ and $(-4, -5)$. The correct response is: $(-1, -2)$ and $(-4, -5)$.