1. The problem asks to identify the correct sequence of transformations that correspond to the coordinate transformation $$(x, y) \to (y, -x + 3)$$ for triangle ABC. 2. First, consider a 90-degree clockwise rotation around the origin. The formula for this rotation is: $$ (x, y) \to (y, -x) $$ This matches the first part of the transformation. 3. Next, the transformation adds 3 to the second coordinate, changing it from $-x$ to $-x + 3$. This corresponds to a translation 3 units up, not left or down. 4. Therefore, the sequence is: a 90-degree clockwise rotation around the origin followed by a translation 3 units up. 5. Among the given options: - "A possible sequence is a 90 degree clockwise rotation around the origin followed by a translation left 3 units" is incorrect because the translation is up, not left. - "A possible sequence is a translation down 3 units followed by a 90 degree clockwise rotation around the origin" is incorrect because the translation is after rotation and is up, not down. - "Two of these" is incorrect because neither option fully matches. Final answer: None of the given options is correct based on the transformation $$(x, y) \to (y, -x + 3)$$. If forced to choose the closest, the first option is partially correct except for the direction of translation.