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 rotating it 270 degrees clockwise, we need to calculate the distance between the rotated endpoints of the segment.
To rotate a point 270 degrees clockwise about the origin (0,0), we can use the following formulas:
x' = x*cos(270°) - y*sin(270°)
y' = x*sin(270°) + y*cos(270°)
Applying these formulas to the first endpoint (0, 4):
x' = 0*cos(270°) - 4*sin(270°) = 0 - (-4) = 4
y' = 0*sin(270°) + 4*cos(270°) = 0 + 0 = 0
Applying the formulas to the second endpoint (3, 4):
x' = 3*cos(270°) - 4*sin(270°) = 0 - (-4) = 4
y' = 3*sin(270°) + 4*cos(270°) = -3 + 0 = -3
The rotated endpoints of the segment are (4, 0) and (4, -3). To find the length of the segment, we can calculate the distance between these two points using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 4)^2 + (-3 - 0)^2)
= √(0^2 + (-3)^2)
= √(0 + 9)
= √9
= 3
Therefore, the length of the segment after rotating it 270 degrees clockwise is 3 units.