Final answer:
The point (9, -4) after reflection across the line y = -x will have new coordinates of (-4, -9), which is found by negating and swapping the original coordinates.
Step-by-step explanation:
The reflection of a point across the line y = -x is found by negating and swapping the coordinates of the point. For the point (9, -4), its reflection across the line y = -x will be (-4, -9). The 'negating and swapping' rule implies that if you have coordinates (x, y), the reflection will be (-y, -x) which ensures the reflected point lies across the line y = -x at an equal distance but on the opposite side. So, the new position of the given point after reflection will be (-4, -9).