1. **Problem Statement:** Determine which statements about the sequence of transformations from the preimage triangle ABC to the image triangle A''B''C'' are true, given the coordinate transformation notation $(x,y) \to (y,-x+3)$. 2. **Understanding the transformation:** The rule $(x,y) \to (y,-x+3)$ means each point $(x,y)$ is mapped to a new point where the new $x$-coordinate is the old $y$-coordinate, and the new $y$-coordinate is $-x+3$. 3. **Step 1: Analyze the transformation as rotation and translation.** - A 90 degree clockwise rotation about the origin transforms $(x,y)$ to $(y,-x)$. - The given transformation adds $+3$ to the $y$-coordinate after rotation, so it is a 90 degree clockwise rotation followed by a translation **up** 3 units. 4. **Check the given statements:** - "A possible sequence is a 90 degree clockwise rotation around the origin followed by a translation left 3 units." - The translation is not left 3 units; the $y$-coordinate is increased by 3, so this is false. - "A possible sequence is a translation down 3 units followed by a 90 degree clockwise rotation around the origin." - Translating down 3 units first would subtract 3 from $y$, then rotating would not produce the $+3$ in the $y$-coordinate after rotation. So this is false. - "Two of these" - Since both above are false, this is false. 5. **Conclusion:** None of the given statements are true about the transformation. **Final answer:** None of the statements are true.