1. The problem asks for the translation rule that maps triangle $\triangle STU$ to $\triangle S'T'U'$.\n2. The given points are:\n- $U(-9,-1)$ to $U'(4,8)$\n- $T(-5,-5)$ to $T'(8,4)$\n- $S(-9,-9)$ to $S'(4,0)$\n3. A translation rule moves every point by the same amount horizontally and vertically. The rule is generally written as $(x,y) \to (x + a, y + b)$ where $a$ is the horizontal shift and $b$ is the vertical shift.\n4. Calculate the horizontal shift $a$ by subtracting the original $x$-coordinate from the translated $x$-coordinate for any point, for example, for point $U$:\n$$a = 4 - (-9) = 4 + 9 = 13$$\n5. Calculate the vertical shift $b$ similarly, for point $U$:\n$$b = 8 - (-1) = 8 + 1 = 9$$\n6. Therefore, the translation rule is:\n$$ (x, y) \to (x + 13, y + 9) $$\nThis means every point of $\triangle STU$ is moved 13 units to the right and 9 units up to get $\triangle S'T'U'$.