1. **State the problem:** We need to determine which transformation among the given options results in an image congruent to its pre-image. 2. **Recall the rule for congruence in transformations:** A transformation is congruent if it preserves distances and angles, meaning it is an isometry. Common isometries include translations, reflections, and rotations. Scaling by factors other than ±1 changes size and is not congruent. 3. **Analyze each transformation:** - $(x, y) \to (-3x, y)$: This multiplies the $x$-coordinate by $-3$, which changes size (scaling by 3) and reflects over the $y$-axis. Not congruent because of scaling. - $(x, y) \to (3x, y - 1)$: This scales $x$ by 3 and translates $y$ by $-1$. Scaling changes size, so not congruent. - $(x, y) \to (-x, y)$: This reflects the point over the $y$-axis (negates $x$), which is an isometry and preserves size and shape. - $(x, y) \to (-x, 3y)$: This reflects $x$ and scales $y$ by 3, changing size. Not congruent. 4. **Conclusion:** The only transformation that results in a congruent image is $(x, y) \to (-x, y)$. **Final answer:** $(x, y) \to (-x, y)$