1. **State the problem:** We have a right triangle on a coordinate plane with a height of 6 units and a base with endpoints at (1, -3) and (8, -3). We need to find the length of the hypotenuse. 2. **Find the length of the base:** The base lies on the line $y = -3$, so the length is the difference in the x-coordinates: $$\text{base} = 8 - 1 = 7$$ 3. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the formula is: $$c = \sqrt{a^2 + b^2}$$ 4. **Substitute the known values:** Here, $a = 6$ (height) and $b = 7$ (base), so: $$c = \sqrt{6^2 + 7^2} = \sqrt{36 + 49} = \sqrt{85}$$ 5. **Conclusion:** The length of the hypotenuse is $\sqrt{85}$ units. **Answer:** Option C. $\sqrt{85}$ units.