To apply the rotation mapping rules for a -270 degrees (clockwise) rotation about the origin, we can use the following transformation for a point \( (x, y) \):
When rotating by \(-270\) degrees (or equivalently \(90\) degrees counterclockwise), the transformation is given by:
\[ (x, y) \rightarrow (y, -x) \]
Now, let's apply this transformation to point \( H \) which is at coordinates \( (-1, -8) \).
- Assign \( x = -1 \) and \( y = -8 \).
- Apply the transformation: \[ (x, y) \rightarrow (y, -x) \rightarrow (-8, 1) \]
Thus, the image of point \( H \) after a -270 degree rotation about the origin is:
\[ \boxed{(-8, 1)} \]