Final answer:
The image of F(-2, 7) after a rotation of 180° clockwise is F'(2, -7).
Step-by-step explanation:
To find the image of a point after a rotation, we can use the formula (x', y') = (xcosθ - ysinθ, xsinθ + ycosθ), where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the image after rotation.
In this case, the original point is F(-2, 7) and we want to rotate it 180° clockwise. This means the rotation angle θ is 180°. Substituting the values into the formula, we get:
(x', y') = (-2cos180° - 7sin180°, -2sin180° + 7cos180°)
After evaluating the trigonometric functions, we find that the image of F(-2, 7) after a rotation of 180° clockwise is F'(2, -7).