To find the image of point H after a -270 degrees clockwise rotation about the origin, we can apply the standard rotation rule for a point (x, y).
The rule for rotating a point (x, y) counterclockwise by an angle θ is given by:
\[ (x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta) \]
For a clockwise rotation, we can use the equivalent negative angle (i.e., -270 degrees is the same as +90 degrees). Therefore, we will apply the rotation for +90 degrees.
In degrees, the rotation angles work out as follows:
- \(\cos(90^\circ) = 0\)
- \(\sin(90^\circ) = 1\)
Applying the rotation transformation to the point H (-1, -8):
- Substitute \(x = -1\) and \(y = -8\): \[ x' = -1 \cdot 0 - (-8) \cdot 1 = 0 + 8 = 8 \] \[ y' = -1 \cdot 1 + (-8) \cdot 0 = -1 + 0 = -1 \]
Thus, after the -270 degrees clockwise rotation, the image of point H is:
\[ H' = (8, -1) \]
So, the final result is:
H' = (8, -1).