Final answer:
The image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin is (6,-4).
Step-by-step explanation:
To find the image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin, we can apply the rotation formula.
The formula for rotating a point (x,y) counterclockwise about the origin by an angle θ is:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Using this formula, we can substitute the values x = -4, y = -6, and θ = 90° to find the new coordinates of the point after the rotation:
x' = -4 * cos(90°) - (-6) * sin(90°) = 6
y' = -4 * sin(90°) + (-6) * cos(90°) = -4
Therefore, the image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin is (6,-4).