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

Answer 1

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 \((-4, -5)\).