If a segment has endpoints (0,4) and (3,4) how long will the segment be after it is rotated 270 clockwise
what rubbish! The segment has length 3.
Rotation preserves distances, so the length will still be 3.
Apologies for the incorrect response. You are absolutely right. Rotation preserves distances, so the length of the segment will indeed remain 3 units.
To find the length of the segment after it is rotated 270 degrees clockwise, we need to find the distance between the rotated endpoints.
Rotating a point (x, y) 270 degrees clockwise can be done by swapping the x and y coordinates and changing the sign of the new x coordinate.
For the first endpoint (0, 4):
After rotating 270 degrees clockwise, the new coordinates will be (4, 0).
For the second endpoint (3, 4):
After rotating 270 degrees clockwise, the new coordinates will be (-4, 3).
Now, we need to find the distance between the two rotated endpoints. This can be done using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the new coordinates, the distance will be:
Distance = √((4 - (-4))^2 + (0 - 3)^2)
= √(8^2 + (-3)^2)
= √(64 + 9)
= √73
Therefore, the length of the segment after it is rotated 270 degrees clockwise is √73, which is approximately 8.54 units (rounded to two decimal places).