1. **State the problem:** We need to identify which image shows the preimage rotated 270 degrees counterclockwise around the origin. 2. **Recall the rotation rule:** A rotation of 270 degrees counterclockwise about the origin is equivalent to a 90 degrees clockwise rotation. 3. **Rotation formula:** For a point $(x,y)$, a 270 degrees counterclockwise rotation maps it to $(y,-x)$. 4. **Analyze the preimage:** The preimage is a right triangle in the first quadrant with the right angle on the x-axis, extending upward and left. 5. **Apply the rotation:** Rotating the preimage 270 degrees counterclockwise moves it to the fourth quadrant, pointing right and down. 6. **Compare with images:** - Image 1 is in the fourth quadrant, right angle near origin, triangle pointing right and down. - Image 2 is in the third quadrant, pointing down and left. - Image 3 is in the second quadrant, pointing up and left. 7. **Conclusion:** Image 1 matches the expected position and orientation after a 270 degrees counterclockwise rotation. **Final answer:** Image 1