Question

reflecting a point over the line $y = x$ involves swapping its _________.
reflecting a figure over the y-axis changes the sign of its _________ coordinates.
translating a figure involves moving it without changing its _________ or shape.
to determine if two triangles are congruent, both their corresponding side lengths and _________ must be the same.

Explanation:

1. For reflection over $y=x$, the rule is $(x,y) \to (y,x)$, so the $x$ and $y$ coordinates are swapped.
2. Reflecting over the y-axis uses the rule $(x,y) \to (-x,y)$, only the $x$-coordinate's sign changes.
3. Translation is a rigid transformation that preserves size, shape, and orientation, only moving the figure.
4. Congruent triangles have all corresponding sides equal (SSS) and all corresponding angles equal (AAA), so both sides and angles must match.

Answer:

1. $x$ and $y$ coordinates
2. $x$- (or horizontal)
3. size
4. corresponding angle measures