Transformations Applied to the Figure

The problem requires determining the final appearance of a figure after two specific geometric transformations:

• Reflection about a horizontal dashed line.
• Rotation by 90° clockwise about an axis perpendicular to the figure's plane.

We will analyze the effect of each transformation step-by-step.

Step 1: Reflection Analysis

The initial figure undergoes a reflection about the specified horizontal dashed line. This transformation flips the figure vertically across the line. Points above the line move below, and points below move above, maintaining the same horizontal position relative to the line of reflection.

Step 2: Rotation Analysis

Next, the reflected figure is subjected to a 90° clockwise rotation. The rotation occurs about an axis perpendicular to the plane of the figure (like spinning a wheel flat on a table). A 90° clockwise rotation changes the orientation significantly:

• An element pointing upwards will point rightwards.
• An element pointing rightwards will point downwards.
• An element pointing downwards will point leftwards.
• An element pointing leftwards will point upwards.

Step 3: Determining the Resultant Figure

By applying the reflection first and then the 90° clockwise rotation to the intermediate shape, we obtain the resultant figure. Comparing the derived final orientation with the provided options, the correct representation is identified.

The sequence of transformations (reflection followed by rotation) leads to a unique final orientation, which matches one of the options presented.