Question: A translation maps $\triangle ABC$ to $\triangle A'B'C'$.\n\n$A'$ \n$B'$ \n$C'$ \n$A$ \n$B$ \n$C$\n\nDetermine the translation.\nUse non-negative numbers.\n\nA translation by ____ units ____\n\ngraph: The triangle in the center-right has vertices $A$ at $(-2, 5)$, $B$ at $(3, 3)$, and $C$ at $(1, -1)$, and the translated triangle in the top-left has vertices $A'$ at $(-7, 5)$, $B'$ at $(-2, 3)$, and $C'$ at $(-4, -1)$; position_hint = center

1. **State the problem:** We are given two triangles $\triangle ABC$ and $\triangle A'B'C'$ with coordinates:\n\n$A(-2,5)$, $B(3,3)$, $C(1,-1)$ and $A'(-7,5)$, $B'(-2,3)$, $C'(-4,-1)$.\n\nWe need to find the translation vector that maps $\triangle ABC$ to $\triangle A'B'C'$.\n\n2. **Recall the translation formula:** A translation moves every point by the same vector $(h,k)$, so for any point $(x,y)$, the image is $(x+h,y+k)$.\n\n3. **Find the translation vector $(h,k)$:**\n\nUsing point $A$ and its image $A'$:\n$$h = x_{A'} - x_A = -7 - (-2) = -7 + 2 = -5$$\n$$k = y_{A'} - y_A = 5 - 5 = 0$$\n\nSo the translation vector is $(-5,0)$.\n\n4. **Check with other points to confirm:**\n\nFor $B$ to $B'$:\n$$x_{B'} = x_B + h = 3 + (-5) = -2$$\n$$y_{B'} = y_B + k = 3 + 0 = 3$$\n\nMatches $B'(-2,3)$.\n\nFor $C$ to $C'$:\n$$x_{C'} = x_C + h = 1 + (-5) = -4$$\n$$y_{C'} = y_C + k = -1 + 0 = -1$$\n\nMatches $C'(-4,-1)$.\n\n5. **Interpret the translation:** The translation moves every point 5 units to the left (since $h=-5$) and 0 units vertically.\n\n6. **Use non-negative numbers as requested:** Since the horizontal shift is to the left, we say the translation is by $5$ units to the left.\n\n**Final answer:**\n\nA translation by $5$ units to the left.