A square is plotted on a coordinate plane. Henry claims that any transformation on the square will preserve the length of its sides. Which of the following transformations could be used to show that Henry's claim is incorrect? Select all that apply. translation of 5 units to the right horizontal stretch by a factor of \( \frac{1}{3} \) dilation by a factor of 2 through the origin rotation of \( 45^{\circ} \) clockwise about the square's center a reflection over the \( x \)-axis

To determine which transformations could disprove Henry's claim that **any** transformation on a square preserves the length of its sides, let's analyze each option: 1. **Translation of 5 units to the right**: - **Effect**: Moves the square without altering its shape or size. - **Conclusion**: Preserves side lengths. 2. **Horizontal stretch by a factor of \( \frac{1}{3} \)**: - **Effect**: Compresses the square horizontally, reducing the length of the sides in the horizontal direction. - **Conclusion**: **Does not preserve** side lengths. 3. **Dilation by a factor of 2 through the origin**: - **Effect**: Scales the square uniformly, increasing the length of all sides by a factor of 2. - **Conclusion**: **Does not preserve** side lengths. 4. **Rotation of \( 45^{\circ} \) clockwise about the square's center**: - **Effect**: Rotates the square without changing its size or shape. - **Conclusion**: Preserves side lengths. 5. **Reflection over the \( x \)-axis**: - **Effect**: Flips the square over the \( x \)-axis without altering its size or shape. - **Conclusion**: Preserves side lengths. **Transformations that change the lengths of the square's sides** are the **horizontal stretch by a factor of \( \frac{1}{3} \)** and the **dilation by a factor of 2 through the origin**. These transformations demonstrate that Henry's claim is incorrect because they alter the side lengths of the square. **Final Answer:** • A horizontal stretch by a factor of \( \frac{1}{3} \) • Dilation by a factor of 2 through the origin