Final answer:
The point (4,-4) is rotated 90 degrees counterclockwise about the origin and ends up at (-4, -4).
Step-by-step explanation:
To find the coordinates of the point after rotating 90 degrees counterclockwise about the origin, we can use the formula:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
Substituting the given values x=4, y=-4, and θ=-90 degrees:
x' = 4*cos(-90) - (-4)*sin(-90)
y' = 4*sin(-90) + (-4)*cos(-90)
Calculating the trigonometric functions, we get:
x' = 4*0 - (-4)*(-1) = 0 - 4 = -4
y' = 4*(-1) + (-4)*0 = -4 + 0 = -4
Therefore, the rotated point is (-4, -4).