To solve the problem of finding the composition of transformations that map trapezoid $ABCD$ to $EHGF$, let's break it down step by step.

Step 1: Reflection Over an Axis

The problem asks to reflect the figure over either the $x$-axis or the $y$-axis. From the image:

• The original trapezoid $ABCD$ is above the x-axis.
• The trapezoid $EHGF$ is also above the x-axis but in a different position.

To align trapezoid $ABCD$ with trapezoid $EHGF$, we should reflect $ABCD$ over the y-axis. This will change the orientation and position of the trapezoid.

Step 2: Translation

After reflecting $ABCD$ over the y-axis, the next step is to translate it.

• Horizontal translation: We can observe that the new trapezoid needs to move to the right by a certain number of units.
• Vertical translation: It appears the trapezoid needs to move up by a certain number of units.

Let’s determine the specific translation:

• Horizontal: The reflection would place the points on the left of the y-axis to the right, which aligns with $EHGF$ horizontally.
• Vertical: The figures appear to be aligned vertically, meaning there might be no need for vertical translation, so $y+0$.

Final Transformation

Thus, the transformation involves:

1. Reflection over the y-axis.
2. Translation $x+4$, $y+0$ (assuming from visual inspection the trapezoid is moved 4 units to the right).

Therefore, the correct answer is to reflect over the y-axis.

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you determine which axis to reflect over when aligning figures?
2. What is the impact of reflection on the coordinates of a shape?
3. How does translation affect the orientation of a figure after reflection?
4. Can a combination of reflection and translation result in a congruent figure?
5. How would you verify the accuracy of your transformations in a problem?

Tip: When working with transformations, always double-check the coordinates of key points after each step to ensure accuracy.