Given a point (2, y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees? (1 point)
To rotate a point counterclockwise about the origin, we can use the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Given the point (2, y) where y is the y-coordinate, and rotating counterclockwise by 270 degrees, we can substitute x = 2, y = y, and theta = 270 degrees into the formulas:
x' = 2 * cos(270) - y * sin(270)
y' = 2 * sin(270) + y * cos(270)
Calculating the trigonometric functions:
cos(270 degrees) = 0
sin(270 degrees) = -1
Substitute the values:
x' = 2 * 0 - y * (-1) = y
y' = 2 * (-1) + y * 0 = -2
Therefore, the new point after rotating counterclockwise by 270 degrees is (y, -2).