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 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

(−2, 1)
and (−5, 4)
left parenthesis negative 2 comma 1 right parenthesis and left parenthesis negative 5 comma 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

Answer 1

To rotate a point \((x, y)\) 90° clockwise around the origin, you can use the transformation \((x, y) \to (y, -x)\).

Let's apply this transformation to both endpoints of the line segment, which are \( (2, -1) \) and \( (5, -4) \).

1. **For the point \( (2, -1) \)**:
\[
(2, -1) \to (-1, -2)
\]

2. **For the point \( (5, -4) \)**:
\[
(5, -4) \to (-4, -5)
\]

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

The correct response is:
\[
(-1, -2) \text{ and } (-4, -5)
\]
or
\[
\text{(−1, −2) and (−4, −5)}
\]