Sumy is working in geometry class and is given figure ABCD in the coordinate plane to reflect. The coordinates of point D are \( (a, b) \) and she reflects the figure over the line \( y=x \). What are the coordinates of the image D '? \( (a,-b) \) \( (b, a) \) \( (-a, b) \) \( (-b,-a) \)

When reflecting a point over the line \( y = x \), the x-coordinate and y-coordinate are swapped. So, if point D has coordinates \( (a, b) \), its reflection D' over the line \( y = x \) will have coordinates \( (b, a) \). Thus, the correct answer is \( (b, a) \). Now, here's some extra knowledge! Swapping those coordinates might seem simple, but it’s a fundamental concept in geometry! This reflection transforms the entire plane in a neat manner, and you can visualize it by imagining a mirror lying along the line \( y = x \). Every point on one side of the line has a corresponding point directly across from it. For applications, consider how this concept is used in computer graphics. When manipulating shapes or images, understanding reflections helps in creating stunning transformations, giving artists the power to flip images, create symmetrical designs, and even generate patterns with ease!