Translation Point R 5036C0

1. **State the problem:** We know that shape X' is a translation of shape X by 3 units to the right and 1 unit down. We are given the coordinates of point R' on shape X' as approximately $$(5, 4)$$. We need to find the original coordinates of point R on shape X. 2. **Recall the translation rule:** If a point $$(x, y)$$ is translated by $$a$$ units to the right and $$b$$ units down, the new coordinates become $$(x + a, y - b)$$. 3. **Apply the rule in reverse:** Since point R' is the image of point R after translation, $$R' = (x + 3, y - 1)$$ where $$(x, y)$$ are the coordinates of point R. 4. **Set up equations:** Given $$R' = (5, 4)$$, we have: $$x + 3 = 5$$ $$y - 1 = 4$$ 5. **Solve for $$x$$ and $$y$$:** $$x = 5 - 3 = 2$$ $$y = 4 + 1 = 5$$ 6. **Conclusion:** The original coordinates of point R are $$(2, 5)$$.