1. **State the problem:** We have parallelogram UVWX with vertices U(-7,-5), V(-4,-1), W(-1,-1), X(-4,-5) and its translation U'V'W'X' with vertices U'(4,1), V'(7,5), W'(10,5), X'(7,1). 2. **Translation rule:** A translation moves every point by the same amount horizontally and vertically. 3. **Find horizontal shift:** Calculate the difference in x-coordinates between U and U': $$4 - (-7) = 4 + 7 = 11$$ 4. **Find vertical shift:** Calculate the difference in y-coordinates between U and U': $$1 - (-5) = 1 + 5 = 6$$ 5. **Write the translation rule:** Every point $(x,y)$ moves to $(x+11, y+6)$. 6. **Check with another vertex:** For V(-4,-1), translated point should be $( -4 + 11, -1 + 6 ) = (7,5)$ which matches V'. **Final answer:** $$ (x,y) \mapsto (x+11, y+6) $$