If a segment has endpoints (0,4) and (3,4), how long will the segment be after it is rotated 270 degrees clockwise?
If a segment has endpoints (0,4) and (3,4), it means the segment is a horizontal line segment on the y-axis with a length of 3 units.
To determine the length of the segment after rotating 270 degrees clockwise, we can think of the segment as a vector.
The initial vector pointing from (0,4) to (3,4) is (3,0).
When we rotate a vector 270 degrees clockwise, it means we need to rotate it 90 degrees counterclockwise.
To rotate a vector 90 degrees counterclockwise, we can swap its x and y coordinates and change the sign of the new y coordinate.
Applying this rotation to the initial vector (3,0), we get the vector (-0,3).
The new vector (-0,3) represents a vertical segment with endpoints at (0,4) and (0,7).
Therefore, the length of the segment after rotating 270 degrees clockwise is 7-4 = 3 units.