A rectangle PQRS has corners P(0,0) A(6,0) Q(6,3) R(0,3). (a) reflect the rectangle in the line y=x. Draw both the object and the image. (b) Find a false undeb reflection. Explain your answer. (c) Always one property that does not change after reflection.

The vertices of the rectangle are $P(0,0)$, $Q(6,0)$, $R(6,3)$, and $S(0,3)$.

For $P(0,0)$: $P'(0,0)$
For $Q(6,0)$: $Q'(0,6)$
For $R(6,3)$: $R'(3,6)$
For $S(0,3)$: $S'(3,0)$

The object is a rectangle $PQRS$ with vertices $P(0,0)$, $Q(6,0)$, $R(6,3)$, $S(0,3)$. Its length is 6 units and its width is 3 units.
The image is a rectangle $P'Q'R'S'$ with vertices $P'(0,0)$, $Q'(0,6)$, $R'(3,6)$, $S'(3,0)$. Its length is 3 units (along the x-axis from $P'$ to $S'$) and its width is 6 units (along the y-axis from $P'$ to $Q'$).
The coordinates of the image are $\boxed{P'(0,0), Q'(0,6), R'(3,6), S'(3,0)}$.

Reflections are isometries, meaning they preserve distances and angles. Therefore, the shape and size of an object do not change under reflection. The statement claims they change, which is incorrect.

Reflections reverse the orientation (or handedness) of an object. For example, a left hand reflects to a right hand. The statement claims orientation does not change, which is incorrect.

The statement is $\boxed{\text{False}}$.
Reflections preserve shape and size, meaning they do not change. However, reflections do change the orientation of an object.

Reflections are rigid transformations. They preserve properties such as distance, angle measures, shape, and size.

One property that does not change under reflection is $\boxed{\text{shape}}$. (Other valid answers include size, angle measures, or distance between points).