Question

reflecting a shape over the line $y = x$ means swapping the \underline{\hspace{3cm}}.\
a transformation that does not change the size or shape of a figure but changes its position is called a \underline{\hspace{3cm}}.\
the process of shifting every point of a shape the same distance in the same direction is called a \underline{\hspace{3cm}}.

Explanation:

First Blank (Reflecting over \( y = x \)):

When reflecting a shape over the line \( y = x \) in the coordinate plane, the rule for the coordinates of a point \( (x, y) \) is that it transforms to \( (y, x) \). So, we swap the \( x \)-coordinate and the \( y \)-coordinate.

A rigid transformation (also called an isometry) is a transformation that does not change the size or shape of a figure, only its position. Examples include translations, reflections, and rotations.

A translation is a type of transformation where every point of a shape is moved the same distance in the same direction. It is a rigid transformation as it preserves the size and shape of the figure.

Answer:

\( x \)-coordinate and \( y \)-coordinate (or "x - and y - coordinates")

Second Blank (Transformation preserving size/shape, changing position):