1. **State the problem:** We are given a rectangle WXYZ with vertices Z(-9,5), W(-6,6), X(-4,0), and Y(-7,-1). We know that the lengths ZY and WX are both $2\sqrt{10}$. We need to find the perimeter of rectangle WXYZ. 2. **Recall the properties of a rectangle:** Opposite sides are equal in length, and the perimeter $P$ is given by $$P = 2(\text{length} + \text{width})$$ 3. **Calculate the length of side ZY:** Use the distance formula between points Z(-9,5) and Y(-7,-1): $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-7 + 9)^2 + (-1 - 5)^2} = \sqrt{2^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40} = 2\sqrt{10}$$ 4. **Calculate the length of side WX:** Given as $2\sqrt{10}$, which matches the problem statement. 5. **Calculate the length of side XY:** Use the distance formula between points X(-4,0) and Y(-7,-1): $$d = \sqrt{(-7 + 4)^2 + (-1 - 0)^2} = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$$ 6. **Calculate the length of side ZW:** Use the distance formula between points Z(-9,5) and W(-6,6): $$d = \sqrt{(-6 + 9)^2 + (6 - 5)^2} = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$$ 7. **Confirm rectangle sides:** Opposite sides are equal: ZY = WX = $2\sqrt{10}$ and ZW = XY = $\sqrt{10}$. 8. **Calculate the perimeter:** $$P = 2(\text{length} + \text{width}) = 2(2\sqrt{10} + \sqrt{10}) = 2(3\sqrt{10}) = 6\sqrt{10}$$ **Final answer:** The perimeter of rectangle WXYZ is $6\sqrt{10}$ units.