1. **State the problem:** We are given a right triangle with vertices W, X, Y, and Z, where the right angle is at vertex W. The lengths of segments YW and XZ are given as expressions $6x + 2$ and $9x - 13$ respectively. We need to find the length of WY. 2. **Identify the right triangle properties:** Since the triangle has a right angle at W, we can use the Pythagorean theorem to relate the sides. The Pythagorean theorem states: $$\text{(hypotenuse)}^2 = \text{(leg}_1)^2 + \text{(leg}_2)^2$$ 3. **Assign sides:** Assuming WY is the hypotenuse, and YW and XZ are the legs, then: $$WY^2 = (YW)^2 + (XZ)^2$$ 4. **Substitute the expressions:** $$WY^2 = (6x + 2)^2 + (9x - 13)^2$$ 5. **Expand the squares:** $$(6x + 2)^2 = 36x^2 + 24x + 4$$ $$(9x - 13)^2 = 81x^2 - 234x + 169$$ 6. **Add the expressions:** $$WY^2 = (36x^2 + 24x + 4) + (81x^2 - 234x + 169) = 117x^2 - 210x + 173$$ 7. **Find WY:** $$WY = \sqrt{117x^2 - 210x + 173}$$ **Final answer:** $$WY = \sqrt{117x^2 - 210x + 173}$$ This expression gives the length of WY in terms of $x$.