To find the image of point H after a rotation of -270 degrees clockwise about the origin, we can use the rotation mapping rules.
The rotation mapping rules state that for a rotation of θ degrees clockwise about the origin, the coordinates (x, y) of any point become (x', y') after the rotation, where:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, the point H has coordinates (x, y) = (3, 4).
Using the rotation mapping rules, we can find the new coordinates (x', y'):
x' = 3 * cos(-270°) - 4 * sin(-270°)
= 3 * cos(-270°) + 4 * cos(90°) (since sin(-x) = -sin(x) and cos(-x) = cos(x))
= 3 * cos(-270°) + 4 * 0
= 3 * cos(90°)
= 3 * 0
= 0
y' = 3 * sin(-270°) + 4 * cos(-270°)
= 3 * sin(-270°) + 4 * sin(90°) (since sin(-x) = -sin(x) and cos(-x) = cos(x))
= 3 * sin(-270°) + 4 * 0
= 3 * sin(90°)
= 3 * 1
= 3
Therefore, the image of point H after a rotation of -270 degrees clockwise about the origin is (0, 3).