Question

Identify the transformation that carries the figure onto itself.

A-rotate 180° clockwise about (-7,-4) and reflect across the line y=-1
B-rotate 180° clockwise about (-7,-4) and reflect across the line x = -7
C-rotate 180° clockwise about (-8,-4) and reflect across the line y = -1
D-rotate 180° clockwise about (-8,-4) and reflect across the line x = -7

Answer 1

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.