1. **State the problem:** We have a rectangle with one side along the line segment between points $(-5,1)$ and $(4,1)$. The perimeter of the rectangle is 26 units. We need to find the coordinates of the other two vertices. 2. **Identify known values:** - One side length is the distance between $(-5,1)$ and $(4,1)$. - The perimeter $P$ of a rectangle is given by $P = 2(\text{length} + \text{width})$. 3. **Calculate the length of the known side:** $$\text{length} = |4 - (-5)| = 4 + 5 = 9$$ 4. **Set up the perimeter equation:** $$26 = 2(9 + w)$$ where $w$ is the width (the unknown side length). 5. **Solve for $w$:** $$26 = 18 + 2w$$ $$26 - 18 = 2w$$ $$8 = 2w$$ $$w = \cancel{\frac{8}{2}} = 4$$ 6. **Determine the coordinates of the other two vertices:** Since the known side is horizontal at $y=1$, the other two vertices must be vertically above or below this line by 4 units. - If the rectangle extends upward, the other vertices are: $$(-5, 1 + 4) = (-5, 5)$$ $$(4, 1 + 4) = (4, 5)$$ - If the rectangle extends downward, the other vertices are: $$(-5, 1 - 4) = (-5, -3)$$ $$(4, 1 - 4) = (4, -3)$$ **Final answer:** The other two vertices are either $(-5,5)$ and $(4,5)$ or $(-5,-3)$ and $(4,-3)$.