Final Answer:
22 ways can a rectangle be reflected across an axis of symmetry so that it carries onto itself. Therefore, the correct option is 2) 22.
Step-by-step explanation:
A rectangle can be reflected across an axis of symmetry in 22 ways. There are 11 different axes of symmetry for a rectangle, and each axis can produce two distinct reflections, resulting in a total of 22 ways for the rectangle to carry onto itself. Rectangles possess symmetry across their horizontal, vertical, and diagonal axes, and these symmetrical properties contribute to the multiple ways they can be reflected.
For a rectangle, the axes of symmetry include the two horizontal sides, two vertical sides, and seven other diagonals that connect opposite corners. Each of these axes can be the line across which the rectangle reflects to coincide with its original shape. When a rectangle is reflected across these axes, it matches up with its original form due to its symmetrical characteristics. This property leads to the 22 different possible reflections that preserve the rectangle's shape onto itself.
Therefore, the total count of reflections for a rectangle across its axes of symmetry amounts to 22 distinct ways, considering the various symmetrical possibilities along its sides and diagonals. Therefore, the correct option is 2) 22.