1. **State the problem:** We need to find the translation rule that maps segment JK to segment J'K'. 2. **Given points:** - J(-5, -5) maps to J'(1, -1) - K(-1, -3) maps to K'(5, 1) 3. **Translation rule formula:** A translation moves every point by adding a fixed vector $(a, b)$ to the original coordinates: $$ (x, y) \mapsto (x + a, y + b) $$ 4. **Find the translation vector $(a, b)$:** Calculate the change in x and y from J to J': $$ a = 1 - (-5) = 1 + 5 = 6 $$ $$ b = -1 - (-5) = -1 + 5 = 4 $$ 5. **Verify with point K:** $$ -1 + 6 = 5 $$ $$ -3 + 4 = 1 $$ This matches K' exactly, confirming the translation vector. 6. **Final translation rule:** $$(x, y) \mapsto (x + 6, y + 4)$$