A line segment has endpoints (2,−1)

Question

and (5, −4)
. What are the new endpoints after rotating the segment 90°
clockwise? (−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)
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

(2, −1)
and (4, 5)

Answer 1

To rotate a point \((x, y)\) 90 degrees clockwise about the origin, you can use the transformation:

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

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

1. For the point \((2, -1)\):

\[ (2, -1) \rightarrow (-1, -2) \]

2. For the point \((5, -4)\):

\[ (5, -4) \rightarrow (-4, -5) \]

So the new endpoints after rotating the segment 90 degrees clockwise are:

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

Therefore, the correct option from the choices given is:

\((-1, -2)\) and \((-4, -5)\).