Final answer:
The length of segment IJ remains the same after reflection. This is because reflections in geometry preserve the size and shape of objects. The lengths of original and reflected segments are equal in Euclidean geometry.
Step-by-step explanation:
When measuring the length IJ before and after reflection, you will notice that the lengths remain equal. A reflection in geometry does not alter the size or shape of the object; it creates a mirror image over a line of reflection. Thus, the reflected segment IJ will have the same length as the original segment IJ. This principle is a part of the properties of reflections in Euclidean geometry, which ensures that the shape and size of figures are preserved during the reflection transformation.
For example, if you measure a segment that is 9.3 cm long and then measure its reflection, you should also find that the reflected segment is 9.3 cm. Any movements within a plane, such as reflections, translations, rotations, and dilations (except for reductions or enlargements), will maintain the congruency of geometric figures.
In the context of wave phenomena and optics, such as with light reflecting off a surface, you might also use a ruler to measure distances related to reflection and refraction. However, in these cases, although the path or angle of the wave changes, the actual measurement of physical lengths with a ruler should remain consistent with the original values unless physical alterations are introduced to the medium or geometry of the system.