1. **State the problem:** We have a right triangle with points J, M, L, and K. Line segment JM is perpendicular to ML, so angle M is 90°. Given: JM = 2, MK = 8, and we need to find $x = ML$. 2. **Identify the right triangle and sides:** Since JM is perpendicular to ML, triangle JML is right-angled at M. 3. **Use the Pythagorean Theorem:** For right triangle JML, the theorem states: $$x^2 = JM^2 + JL^2$$ 4. **Find JL:** Note that JL = JM + MK = 2 + 8 = 10. 5. **Substitute values:** $$x^2 = 2^2 + 10^2$$ $$x^2 = 4 + 100$$ $$x^2 = 104$$ 6. **Solve for x:** $$x = \sqrt{104} = 2\sqrt{26}$$ **Final answer:** $$x = 2\sqrt{26}$$