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

Henry's claim can be challenged by certain transformations that change the dimensions of the square. The horizontal stretch by a factor of \( \frac{1}{3} \) would compress the square's width, thus altering its side lengths and proving Henry's claim incorrect. Similarly, a dilation by a factor of 2 through the origin would enlarge the square and also change the lengths of its sides, making it a valid example. On the other hand, transformations like translation, rotation, or reflection do not affect the lengths of the sides of the square. They merely reposition or reorient the square without stretching, shrinking, or altering its dimensions in a way that affects the lengths.