To rotate a point counterclockwise by 90 degrees around the origin, you can use the following transformation on the coordinates \((x, y)\):
\[ (x, y) \rightarrow (-y, x) \]
For the point \(D(-4, -9)\):
- \(x = -4\)
- \(y = -9\)
Applying the transformation:
\[ D' = (-(-9), -4) = (9, -4) \]
So, after a 90-degree counterclockwise rotation, the new coordinates of point \(D'\) would be \((9, -4)\).