Given a point (x,y) which is the new point when the point is rotated counterclockwise about the origin 270 degrees
To rotate a point counterclockwise about the origin, we can use the following rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, we want to rotate the point (x, y) by 270 degrees counterclockwise, so theta = 270 degrees. Converting 270 degrees to radians, we get theta = 3π/2.
Substituting the values into the rotation formula:
x' = x * cos(3π/2) - y * sin(3π/2)
y' = x * sin(3π/2) + y * cos(3π/2)
Now, we can simplify these equations:
x' = x * 0 - y * (-1) = y
y' = x * (-1) + y * 0 = -x
Therefore, the new point (x', y') when the point (x, y) is rotated counterclockwise about the origin by 270 degrees is (y, -x).
To find the new point after rotating (x, y) counterclockwise about the origin by 270 degrees, you can use the following steps:
1. Convert the rotation angle from degrees to radians. Since 270 degrees is equivalent to 3/2π radians (or -π/2 radians), we'll use -π/2 for the rotation angle.
2. Apply the rotation formula for counterclockwise rotation about the origin:
new_x = x * cos(rotation_angle) - y * sin(rotation_angle)
new_y = x * sin(rotation_angle) + y * cos(rotation_angle)
3. Substitute the values into the formula:
new_x = x * cos(-π/2) - y * sin(-π/2)
= x * 0 - y * (-1)
= y
new_y = x * sin(-π/2) + y * cos(-π/2)
= x * (-1) + y * 0
= -x
Therefore, the new point after rotating (x, y) counterclockwise about the origin by 270 degrees is (-y, -x).