Question

How would you describe the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II to show that the rectangles are congruent? (1 point)

reflection, then translation

translation, then rotation

Rotation, then reflection

Rotation, then translation

Answer 1

To determine the correct series of transformations that move a rectangle in Quadrant IV to a rectangle in Quadrant II while ensuring they are congruent, we can analyze the transformations one by one.

1. **Reflection**: A reflection across the y-axis would move a shape in Quadrant IV (where x is negative and y is negative) to Quadrant II (where x is negative and y is positive).

2. **Translation**: A translation would move the rectangle without changing its orientation, which would not help in this case since it would not cause a change from Quadrant IV to Quadrant II.

3. **Rotation**: A rotation around a point would generally involve changing the positions of points in a way that might not lead directly to the opposite quadrant without a reflection.

Given that the rectangle in Quadrant IV needs to be flipped to be in Quadrant II, the most straightforward transformation is by reflecting it across the y-axis.

Thus, the correct answer is:

**Reflection, then translation** (in the sense that a reflection would position the figure in a manner that could still be translated if needed, but solely reflection suffices here).