given a point (x, y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees???
When a point (x, y) is rotated counterclockwise about the origin by 270 degrees, it is equivalent to rotating it clockwise by 90 degrees.
To find the new coordinates of the point, we can use the rotation formula:
For a clockwise rotation of (x, y) by angle θ, the new coordinates (x', y') can be obtained using the following formulas:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
In this case, since we are rotating counterclockwise by 90 degrees (or clockwise by -90 degrees), we substitute θ = -90 degrees.
x' = x*cos(-90) - y*sin(-90)
y' = x*sin(-90) + y*cos(-90)
Note: In trigonometry, cos(-θ) = cos(θ) and sin(-θ) = -sin(θ), which simplifies the expressions further.
x' = x*cos(-90) - y*sin(-90) = x*0 - y*(-1) = y
y' = x*sin(-90) + y*cos(-90) = x*(-1) + y*0 = -x
Therefore, the new point after rotating (x, y) counterclockwise about the origin by 270 degrees is (-y, -x).