If a segment has endpoints (0, 4) and (3, 4), how long will the segment be after it is rotated 270° clockwise?
(1 point)
If a segment is rotated 270° clockwise, the endpoints of the segment will also rotate 270° clockwise. This means that the point (0,4) will be rotated to (4,0) and the point (3,4) will be rotated to (4,-3).
To find the length of the segment after rotation, we can use the distance formula. The distance formula states that the distance between two points (x1,y1) and (x2,y2) is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the first point after rotation is (4,0) and the second point after rotation is (4,-3).
Using the distance formula, we can calculate the distance:
distance = √((4 - 4)^2 + (0 - (-3))^2)
= √((0)^2 + (3)^2)
= √(0 + 9)
= √9
= 3
Therefore, the segment will be 3 units long after it is rotated 270° clockwise.