A line segment has endpoints (2,−1) and (5, −4). What are the new endpoints after rotating the segment 90° clockwise?(1 point)
Responses
To rotate a point (x, y) 90° clockwise, we can use the following formulas:
New x-coordinate = y
New y-coordinate = -x
Let's apply these formulas to find the new endpoints:
For the first endpoint (2, -1):
New x-coordinate = -1
New y-coordinate = -2
So, the new coordinates for the first endpoint after rotating it 90° clockwise are (-1, -2).
For the second endpoint (5, -4):
New x-coordinate = -4
New y-coordinate = -5
So, the new coordinates for the second endpoint after rotating it 90° clockwise are (-4, -5).
Therefore, the new endpoints of the line segment after rotating it 90° clockwise are (-1, -2) and (-4, -5).
"..after rotating the segment 90° clockwise"
rotating about what ?
question can't be answered.
To find the new endpoints after rotating the line segment 90° clockwise, you can follow these steps:
1. Determine the midpoint of the line segment.
- The midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
- In this case, the midpoint is calculated as follows:
Midpoint (xm, ym) = ((2 + 5)/2, (-1 + -4)/2) = (7/2, -5/2) = (3.5, -2.5)
2. Translate the endpoints so that the midpoint becomes the origin.
- This is done by subtracting the coordinates of the midpoint from the original endpoints.
- The translated endpoints can be calculated as:
Translated endpoint 1 = (2, -1) - (3.5, -2.5) = (-1.5, 1.5)
Translated endpoint 2 = (5, -4) - (3.5, -2.5) = (1.5, -1.5)
3. Rotate the translated endpoints 90° clockwise around the origin.
- To rotate a point (x, y) 90° clockwise, swap the x and y coordinates and negate the new x coordinate.
- Applying this to the translated endpoints:
Rotated endpoint 1 = (-1.5, 1.5) becomes (1.5, 1.5)
Rotated endpoint 2 = (1.5, -1.5) becomes (-1.5, -1.5)
4. Translate the rotated endpoints back to their original position.
- Add the coordinates of the midpoint to the rotated endpoints.
- The final endpoints after rotating the line segment 90° clockwise are:
Final endpoint 1 = (1.5, 1.5) + (3.5, -2.5) = (5, -1)
Final endpoint 2 = (-1.5, -1.5) + (3.5, -2.5) = (2, -4)
Therefore, the new endpoints after rotating the line segment 90° clockwise are (5, -1) and (2, -4).