Final answer:
The image of point W (-5, -3) after a 270-degree counterclockwise rotation is (5, -3).
Step-by-step explanation:
To find the image of point W after a 270-degree counterclockwise rotation, we can use the rotation matrix. The rotation matrix for a counterclockwise rotation of angle θ is:
[cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
Plugging in θ = 270 degrees:
[cos(270) -sin(270)]
[sin(270) cos(270)]
Simplifying the matrix gives:
[0 1]
[-1 0]
If we multiply the matrix [0 1] with the coordinates of point W (-5, -3), we get the image coordinates after the rotation:
0*(-5) + 1*(-3) = -3
-1*(-5) + 0*(-3) = 5
Therefore, the image of point W (-5, -3) after a 270-degree counterclockwise rotation is (5, -3).