Given a point on a geometric figure (x,%C2%A0y) , what is the new point when the figure is rotated clockwise about the origin 270 degrees
To find the new point after rotating the point (x, y) 270 degrees clockwise about the origin, we can use the following rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
where theta is the angle of rotation in radians (270 degrees in this case).
Converting 270 degrees to radians:
270 degrees * (π/180) = 3π/2 radians
Substitute x = x, y = y, and theta = 3π/2 into the rotation formula:
x' = x * cos(3π/2) - y * sin(3π/2)
y' = x * sin(3π/2) + y * cos(3π/2)
Calculate the cosine and sine of 3π/2:
cos(3π/2) = 0
sin(3π/2) = -1
Substitute these values back into the rotation formula:
x' = x * 0 - y * (-1) = y
y' = x * (-1) + y * 0 = -x
Therefore, the new point after rotating (x, y) 270 degrees clockwise about the origin is (-y, -x).