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A line segment has endpoints (2,−1)

and (5, −4)
. What are the new endpoints after rotating the segment 90°
clockwise?(1 point)
Responses

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

(−2, 1)
and (−5, 4)

2 answers

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

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

Now, we will apply this transformation to both endpoints of the line segment.

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

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

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

Therefore, the correct response is:

\((−1, −2)\) and \((−4, −5)\).

A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units