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

To determine which transformations could show that Henry's claim is incorrect, we need to analyze each transformation in terms of whether it preserves the properties of the square, such as shape, size, and orientation. 1. **Translation of 5 units to the right**: - A translation moves every point of the square the same distance in a specified direction. This transformation preserves the shape and size of the square. - **Conclusion**: This transformation does not show that Henry's claim is incorrect. 2. **Dilation by a factor of 2 through the origin**: - Dilation changes the size of the square while keeping the shape the same. A factor of 2 means the square will become larger, but it will still be a square. - **Conclusion**: This transformation does not show that Henry's claim is incorrect. 3. **Dilation by a factor of \( \frac{1}{3} \)**: - Similar to the previous dilation, this transformation reduces the size of the square but maintains its shape. - **Conclusion**: This transformation does not show that Henry's claim is incorrect. 4. **Reflection over the \( x \)-axis**: - A reflection flips the square over the \( x \)-axis, which preserves the shape and size but changes the orientation. - **Conclusion**: This transformation does not show that Henry's claim is incorrect. 5. **Rotation \( 45^{\circ} \) clockwise about the square's center**: - A rotation changes the orientation of the square but preserves its shape and size. - **Conclusion**: This transformation does not show that Henry's claim is incorrect. Based on the analysis, none of the transformations listed would show that Henry's claim is incorrect, as all of them preserve the properties of the square. If the goal is to show that a transformation can change the properties of the square, we would need a transformation that alters the shape or size, such as a non-uniform scaling or a shear transformation. However, none of the provided options fit that criterion.