Final answer:
The necessary details to establish the scale factor for segments OX' and Oy are missing from the provided information, therefore the question cannot be answered accurately.
Step-by-step explanation:
To determine the lengths of segments OX' and Oy, we first need to establish the scale factor. There are various scale factors mentioned in the information provided, but we must identify the specific scale factor applicable to the question concerning OX' and Oy. Unfortunately, the actual dimensions and other necessary information to conclude on OX' and Oy are not detailed explicitly in the question. Hence, based on the given information, we cannot confidently provide the correct lengths for segments OX' and Oy or calculate the particular scale factor required.