Question
If a segment has endpoint, zero, four and three, four, how long will the segment be after it is rotated 270° clockwise
Answers
GPT 3.5
To find the new length of the segment after it is rotated 270° clockwise, we can use the distance formula in the coordinate plane.
We have the initial endpoints of the segment as (0,4) and (3,4).
After rotating 270° clockwise, the new endpoints will be (-4, 0) and (-4, 3).
Using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
d = √((-4 - 0)^2 + (3 - 4)^2)
d = √((-4)^2 + (-1)^2)
d = √(16 + 1)
d = √17
Therefore, the length of the segment after it is rotated 270° clockwise is sqrt(17) units.
We have the initial endpoints of the segment as (0,4) and (3,4).
After rotating 270° clockwise, the new endpoints will be (-4, 0) and (-4, 3).
Using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
d = √((-4 - 0)^2 + (3 - 4)^2)
d = √((-4)^2 + (-1)^2)
d = √(16 + 1)
d = √17
Therefore, the length of the segment after it is rotated 270° clockwise is sqrt(17) units.