A line segment has endpoints (2,−1) and (5, −4) . What are the new endpoints after rotating the segment 90° clockwise?

Question

1. (−2, −1) and (−5, −4)
2. (−2, 1) and (−5, 4)
3. (2, −1) and (4, 5)
4. (−1, −2) and (−4, −5)

Answer 1

To rotate a point \((x, y)\) by \(90^\circ\) clockwise around the origin, you use the transformation:

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

Now 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 after rotating the endpoints \( (2, -1) \) and \( (5, -4) \) \(90^\circ\) clockwise, the new endpoints are \((-1, -2)\) and \((-4, -5)\).

Thus, the correct answer is:

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