What is the image of \( (2,4) \) after a reflection over the \( x \)-axis?

Reflecting a point over the \( x \)-axis means that we keep the \( x \)-coordinate the same and change the sign of the \( y \)-coordinate. For the point \( (2, 4) \), the \( x \)-coordinate remains \( 2 \), while the \( y \)-coordinate changes from \( 4 \) to \( -4 \). Therefore, the image of \( (2, 4) \) after a reflection over the \( x \)-axis is \( (2, -4) \). When dealing with reflections, it’s always fun to visualize it! Imagine flipping the point across the \( x \)-axis like a pancake flip—upside down but still maintaining its horizontal position. If you place a mirror along the axis, the point's new location reveals itself on the opposite side. Reflecting points can also pop up in real life! For example, if you're designing graphics or animations, understanding reflections can help you create symmetrical designs. And in physics, reflecting light or sound waves off surfaces can lead to marvelous effects!