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 (−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 formula to use is:

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

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

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

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

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

Thus, the correct response is:

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