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, the new coordinates (x', y') can be found using the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, since we are rotating 270 degrees counterclockwise, we can substitute theta with 270 degrees (or π/2 in radians).
x' = x * cos(270) - y * sin(270)
y' = x * sin(270) + y * cos(270)
Using the trigonometric values for 270 degrees:
cos(270) = 0
sin(270) = -1
The formulas become:
x' = x * 0 - y * (-1) = y
y' = x * (-1) + y * 0 = -x
Therefore, the new point after rotating (x, y) 270 degrees counterclockwise about the origin is (-y, -x).