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 (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 (−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 (−5, 4)

Answer 1

To find the new endpoints of the line segment after rotating it 90° clockwise, we can use the rotation transformation.

The general rule for rotating a point \((x, y)\) 90° clockwise around the origin is:

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

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

1. First endpoint: (2, -1) \[ (2, -1) \rightarrow (-1, -2) \]

2. Second endpoint: (5, -4) \[ (5, -4) \rightarrow (-4, -5) \]

Therefore, after rotating the segment 90° clockwise, the new endpoints are: \[ (-1, -2) \text{ and } (-4, -5) \]

The correct response is: (−1, −2) and (−4, −5).