1. **State the problem:** We have points $X(-2,-2)$ and $X'(-1,0)$, and points $Y(-6,1)$ and $Z(-4,2)$. Points $Y$ and $Z$ are translated by the same vector that moves $X$ to $X'$. We need to find the coordinates of $Y'$ and $Z'$ after this translation. 2. **Find the translation vector:** The translation vector $\vec{v}$ is the difference between $X'$ and $X$: $$\vec{v} = (x', y') - (x, y) = (-1, 0) - (-2, -2)$$ $$\vec{v} = (-1 + 2, 0 + 2) = (1, 2)$$ 3. **Apply the translation vector to $Y$ and $Z$:** For $Y'$, add $\vec{v}$ to $Y$: $$Y' = (-6, 1) + (1, 2) = (-6 + 1, 1 + 2) = (-5, 3)$$ For $Z'$, add $\vec{v}$ to $Z$: $$Z' = (-4, 2) + (1, 2) = (-4 + 1, 2 + 2) = (-3, 4)$$ 4. **Final answer:** $$Y' = (-5, 3), \quad Z' = (-3, 4)$$ This means points $Y$ and $Z$ have been translated by the vector $(1, 2)$, the same as $X$ to $X'$.