What transformation is performed when a student adds 5 to each x-coordinate and 3 to each y-coordinate of a geometric shape?

When a student adds 5 to each x-coordinate and 3 to each y-coordinate of a geometric shape, the transformation being performed is a translation.

Translation refers to shifting a geometric figure from one location to another without changing its shape, size, or orientation. In this case, adding 5 to each x-coordinate moves the entire shape 5 units to the right, while adding 3 to each y-coordinate moves it 3 units up. The result is a new position of the shape that is parallel to its original position, leaving its dimensions and angles unchanged.

Other types of transformations like reflection, rotation, or refraction do not involve simply shifting the positions of points in this manner; instead, they change the orientation or direction of the shape in various ways. Reflection flips the figure over a line, rotation spins it around a point, and refraction typically refers to the bending of light rather than geometric shapes. Thus, the addition of constants to x and y coordinates clearly defines a translation.