If an object is reflected twice over parallel lines, and corresponding points of the original and final translation image are 30 centimeters apart, how far apart are the parallel lines?

To find the distance between the parallel lines, we need to understand how multiple reflections affect the positioning of an object.

Each reflection over a line creates a new image that is equidistant from the line of reflection as the original point. When an object is reflected twice, the final image is equidistant from both reflection lines.

In this case, let's call the first reflection line "Line A" and the second line "Line B." The original point and its corresponding final image are 30 centimeters apart. Since the final image is equidistant from both Line A and Line B, the distance from the final image to Line A is also 30 centimeters.

To determine the distance between the parallel lines, we need to consider that the distance from Line A to the final image is equal to the distance from Line B to the final image. Since these distances are both 30 centimeters, the distance between Line A and Line B is twice that, or 60 centimeters.

Therefore, the parallel lines are 60 centimeters apart.