1. **State the problem:** Find the perimeter of triangle VUW with vertices V(-5,7), U(0,6), and W(0,-1). 2. **Formula:** The perimeter of a triangle is the sum of the lengths of its sides. 3. **Distance formula:** To find the length between two points $(x_1,y_1)$ and $(x_2,y_2)$, use: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 4. **Calculate each side length:** - Side VU: $$d_{VU} = \sqrt{(0 - (-5))^2 + (6 - 7)^2} = \sqrt{5^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26}$$ - Side UW: $$d_{UW} = \sqrt{(0 - 0)^2 + (-1 - 6)^2} = \sqrt{0 + (-7)^2} = \sqrt{49} = 7$$ - Side WV: $$d_{WV} = \sqrt{(0 - (-5))^2 + (-1 - 7)^2} = \sqrt{5^2 + (-8)^2} = \sqrt{25 + 64} = \sqrt{89}$$ 5. **Sum the side lengths to find perimeter:** $$P = \sqrt{26} + 7 + \sqrt{89}$$ 6. **Approximate values:** $$\sqrt{26} \approx 5.10, \quad \sqrt{89} \approx 9.43$$ $$P \approx 5.10 + 7 + 9.43 = 21.53$$ **Final answer:** The perimeter of triangle VUW is approximately **21.53 units**.