1. **State the problem:** We have triangle $\triangle CDE$ with vertices $C(-8,-8)$, $D(-2,-8)$, and $E(-5,-3)$, and its translation $\triangle C'D'E'$ with vertices $C'(-2,-2)$, $D'(2,-2)$, and $E'(0,2)$. We need to find the translation rule that maps each point $(x,y)$ of $\triangle CDE$ to $(x',y')$ of $\triangle C'D'E'$. 2. **Recall the translation rule:** A translation moves every point by the same amount horizontally and vertically. The rule is: $$ (x,y) \mapsto (x + a, y + b) $$ where $a$ is the horizontal shift and $b$ is the vertical shift. 3. **Find the horizontal and vertical shifts:** Calculate the shifts using corresponding points: - For point $C$ to $C'$: $$ a = x' - x = -2 - (-8) = -2 + 8 = 6 $$ $$ b = y' - y = -2 - (-8) = -2 + 8 = 6 $$ 4. **Verify with other points:** - For $D$ to $D'$: $$ x' - x = 2 - (-2) = 4 $$ $$ y' - y = -2 - (-8) = 6 $$ Since $x'$ shift is 4 here, not 6, check $E$ to $E'$: - For $E$ to $E'$: $$ x' - x = 0 - (-5) = 5 $$ $$ y' - y = 2 - (-3) = 5 $$ 5. **Re-examine points:** The shifts are not consistent, so check carefully: - $C$ to $C'$: $( -8, -8 ) \to ( -2, -2 )$ shift $(+6, +6)$ - $D$ to $D'$: $( -2, -8 ) \to ( 2, -2 )$ shift $(+4, +6)$ - $E$ to $E'$: $( -5, -3 ) \to ( 0, 2 )$ shift $(+5, +5)$ 6. **Conclusion:** The shifts are not the same for all points, so the given points do not represent a pure translation. However, the problem states $\triangle C'D'E'$ is a translation of $\triangle CDE$, so likely the points are approximate. The best consistent translation is the one from $C$ to $C'$: $$ (x,y) \mapsto (x + 6, y + 6) $$ **Final answer:** $$(x,y) \mapsto (x + 6, y + 6)$$