1. **State the problem:** We are given three points $N(-3,1)$, $O(-3,-7)$, and $P(1,-5)$ that form a triangle. We need to find the perimeter of this triangle. 2. **Recall the formula:** The perimeter of a triangle is the sum of the lengths of its sides. To find the length between two points $(x_1,y_1)$ and $(x_2,y_2)$, use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate each side length:** - Length $NO$: $$NO = \sqrt{(-3 - (-3))^2 + (-7 - 1)^2} = \sqrt{0^2 + (-8)^2} = \sqrt{64} = 8$$ - Length $OP$: $$OP = \sqrt{(1 - (-3))^2 + (-5 - (-7))^2} = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20}$$ - Length $PN$: $$PN = \sqrt{(1 - (-3))^2 + (-5 - 1)^2} = \sqrt{4^2 + (-6)^2} = \sqrt{16 + 36} = \sqrt{52}$$ 4. **Simplify the square roots:** $$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \approx 4.472$$ $$\sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \approx 7.211$$ 5. **Find the perimeter:** $$\text{Perimeter} = NO + OP + PN = 8 + 4.472 + 7.211 = 19.683$$ 6. **Round to the nearest tenth:** $$19.7$$ **Final answer:** The perimeter of triangle $NOP$ is approximately $19.7$ units.