The image of point A(7, -6) after a reflection in the line y = -x and then in x = 3 will be the point A''(12, -7).
The question asks about the resulting coordinates of point A after it undergoes two reflections, first in the line y = -x, and then in the line x = 3. The initial point is A(7, -6).
Reflection in y = -x: This reflection essentially swaps the x and y coordinates and changes their signs. Therefore, after this reflection, the point A becomes A'(-6, -7).
Reflection in x = 3: This reflection flips the point across the vertical line x = 3. To find the image of point A' after this reflection, calculate its horizontal distance to x = 3, which is 3 - (-6) = 9 units. The image will be the same distance on the other side of the line x = 3, so the x-coordinate will be 3 + 9 = 12. The y-coordinate remains the same. Thus, after this reflection, the point A' becomes A''(12, -7).
The image of the point A(7, -6) after the described transformations is A''(12, -7).