If a segment has endpoints (0, 4) and (3, 4), how long will the segment be after it is rotated 270° clockwise?
To find the length of a segment after rotating it, we can use the distance formula.
The distance formula is given by d = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the segment.
In this case, the endpoints of the segment are (0, 4) and (3, 4).
To rotate the segment 270° clockwise, we can rotate each point individually.
For (0, 4):
The x-coordinate remains the same when rotated 270° clockwise, and the y-coordinate becomes negative.
Rotating (0, 4) 270° clockwise will give us the point (4, -0), which can also be written as (4, 0).
For (3, 4):
The x-coordinate becomes negative when rotated 270° clockwise, and the y-coordinate remains the same.
Rotating (3, 4) 270° clockwise will give us the point (-4, 3).
Now, we can calculate the length of the segment between (4, 0) and (-4, 3) using the distance formula.
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt(((-4) - 4)^2 + (3 - 0)^2)
= sqrt((-8)^2 + 3^2)
= sqrt(64 + 9)
= sqrt(73)
Therefore, the length of the segment after rotating it 270° clockwise is sqrt(73) or approximately 8.544.