Asked by Exoctic_DrEaMs
Given a point (x, y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees
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Answered by
GPT 3.5
To find the new point after rotating counterclockwise about the origin 270 degrees, we can use the following formulas:
New x-coordinate = x * cos(θ) - y * sin(θ)
New y-coordinate = x * sin(θ) + y * cos(θ)
In this case, θ is equal to 270 degrees.
Therefore, the new point is:
New x-coordinate = x * cos(270) - y * sin(270)
= x * 0 - y * (-1)
= 0 + y
= y
New y-coordinate = x * sin(270) + y * cos(270)
= x * (-1) + y * 0
= -x
Thus, the new point after rotating counterclockwise about the origin by 270 degrees is (-y, -x).
New x-coordinate = x * cos(θ) - y * sin(θ)
New y-coordinate = x * sin(θ) + y * cos(θ)
In this case, θ is equal to 270 degrees.
Therefore, the new point is:
New x-coordinate = x * cos(270) - y * sin(270)
= x * 0 - y * (-1)
= 0 + y
= y
New y-coordinate = x * sin(270) + y * cos(270)
= x * (-1) + y * 0
= -x
Thus, the new point after rotating counterclockwise about the origin by 270 degrees is (-y, -x).
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