If a segment has endpoints (0, 4) and (3, 4). How long will the segment be after it is rotated 270 degrees clockwise
To find the length of the segment after it is rotated 270 degrees clockwise, we can use the distance formula.
The distance formula is: √((x2 - x1)^2 + (y2 - y1)^2)
Given the endpoints (0, 4) and (3, 4), the x-coordinates and y-coordinates of the endpoints are:
x1 = 0, y1 = 4
x2 = 3, y2 = 4
When a point is rotated 270 degrees clockwise, its new coordinates can be found using the following formulas:
x' = x*cos(270) - y*sin(270)
y' = x*sin(270) + y*cos(270)
Since our segment is horizontal (the y-coordinates of both endpoints are the same), after rotating 270 degrees clockwise, the new segment will also be horizontal. Therefore, the difference in x-coordinates will give us the length of the segment after rotation.
Using the formulas above, we can calculate the new x-coordinate for the first endpoint:
x' = 0*cos(270) - 4*sin(270) = 0 + 4 = 4
Using the formulas above, we can calculate the new x-coordinate for the second endpoint:
x' = 3*cos(270) - 4*sin(270) = 0 - 4 = -4
The length of the segment after rotation is the difference between the new x-coordinates:
Length = |x2' - x1'| = |-4 - 4| = |-8| = 8
Therefore, the length of the segment after it is rotated 270 degrees clockwise is 8 units.