It appears that you've uploaded an image related to a geometry problem involving the transformation of a triangle on a graph. Based on the details visible in the image, the problem involves identifying correct statements about the transformation and properties of a triangle $\triangle MNO$ and its image $\triangle M'N'O'$.

Would you like me to explain why each statement is correct, or help you further analyze the transformations shown?

Here are a few possible questions to expand this topic:

1. How can we prove that $m\angle LM'O'N' = 90^\circ$ geometrically or algebraically?
2. How is the equality $M'N' = MN$ verified using coordinates or distance formula?
3. What is the transformation rule $(x, y) \to (y, x)$, and how does it affect the orientation and size of the triangle?
4. How does a $180^\circ$ rotation about the origin affect all the coordinates of a triangle?
5. How would this transformation look if applied to a different figure, such as a square or a polygon?

Tip:

For verifying geometric transformations, using the distance formula and angle rules in conjunction with coordinate analysis is an excellent way to confirm properties like congruence and orientation. Let me know how you'd like to proceed!