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 a segment that has been rotated, we need to use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the endpoints of the segment are (0,4) and (3,4). Let's label them as (x1, y1) and (x2, y2) respectively.
x1 = 0
y1 = 4
x2 = 3
y2 = 4
Now, let's calculate the length of the segment using the distance formula:
d = √((3 - 0)^2 + (4 - 4)^2)
= √(3^2 + 0^2)
= √9
= 3
Therefore, the length of the segment after rotating it 270 degrees clockwise remains the same at 3 units.
When a segment is rotated 270 degrees clockwise, it becomes vertical with the two endpoints (3,4) and (3,0).
To find the length of this new segment, we can use the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Using the coordinates (3,4) and (3,0), we get:
d = sqrt((3-3)^2 + (0-4)^2)
d = sqrt(16)
d = 4
Therefore, the length of the segment after it is rotated 270 degrees clockwise is 4 units.
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 the segment after it is rotated 270 degrees clockwise, we need to calculate the distance between the new endpoints.
The given endpoints of the segment are (0,4) and (3,4).
To rotate a point P(x, y) 270 degrees clockwise, we can use the following formula:
x' = y
y' = -x
Using this formula, we can calculate the new endpoints:
For the first endpoint (0,4):
x' = 4
y' = 0
For the second endpoint (3,4):
x' = 4
y' = -3
Now, we can use the distance formula to find the length of the new segment:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the new endpoints, the length of the rotated segment can be calculated as:
d = sqrt((4 - 4)^2 + (-3 - 0)^2)
= sqrt(0 + 9)
= sqrt(9)
= 3
Therefore, the length of the segment after it is rotated 270 degrees clockwise is 3 units.