1. **State the problem:** We are given four vectors $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, and $\mathbf{d}$ with the sum $\mathbf{a} + \mathbf{b} + \mathbf{c} + \mathbf{d} = \langle -1, -3 \rangle$. 2. **Goal:** Add the four vectors graphically in a different order and verify the resultant vector. 3. **Recall vector addition rules:** Vector addition is commutative and associative, meaning the order of addition does not affect the resultant vector. 4. **Given vectors approximate coordinates:** - $\mathbf{a} \approx \langle 1, -2 \rangle$ - $\mathbf{b} \approx \langle 4, -4 \rangle$ - $\mathbf{c} \approx \langle -3, -1 \rangle$ - $\mathbf{d} \approx \langle -3, -1 \rangle$ 5. **Add vectors in original order:** $$\mathbf{a} + \mathbf{b} + \mathbf{c} + \mathbf{d} = \langle 1, -2 \rangle + \langle 4, -4 \rangle + \langle -3, -1 \rangle + \langle -3, -1 \rangle$$ 6. **Calculate component-wise sum:** $$= \langle 1 + 4 - 3 - 3, -2 - 4 - 1 - 1 \rangle = \langle -1, -8 \rangle$$ 7. **Note:** The problem states the sum is $\langle -1, -3 \rangle$, so the given vector $\mathbf{d}$ in the problem's description might differ from the approximate coordinates here. We will trust the problem's stated sum. 8. **Add vectors in a different order:** For example, add $\mathbf{c} + \mathbf{a} + \mathbf{d} + \mathbf{b}$: $$\mathbf{c} + \mathbf{a} + \mathbf{d} + \mathbf{b} = \langle -3, -1 \rangle + \langle 1, -2 \rangle + \langle -3, -1 \rangle + \langle 4, -4 \rangle$$ 9. **Calculate component-wise sum:** $$= \langle -3 + 1 - 3 + 4, -1 - 2 - 1 - 4 \rangle = \langle -1, -8 \rangle$$ 10. **Conclusion:** The resultant vector is the same regardless of the order of addition, confirming vector addition properties. **Final answer:** The sum of the four vectors in any order is $\langle -1, -3 \rangle$ as given by the problem statement.