Final answer:
To determine which transformation maps a figure onto itself, we must consider a 180° rotation followed by a reflection. Option B, which combines a 180° rotation about the point (-7,-4) with a reflection across the line x = -7, would fulfill this requirement by flipping the figure about the axis of rotation.
This correct answer is B.
Step-by-step explanation:
The question asks to identify the transformation that carries the figure onto itself.
- 180° rotation about a point effectively turns the figure upside down.
- A reflection across a line like y = k or x = h flips the figure across that line.
When combining a 180° rotation about a point with a reflection, we ensure the figure maps onto itself.
For example, a 180° clockwise rotation about the point (-7,-4) followed by a reflection across the line x = -7 (option B) would mean the figure is first turned upside down and then flipped across the x-coordinate of the center of rotation.
Hence, the original and final positions would coincide, mapping the figure onto itself.
This correct answer is B.