1. **State the problem:** We are given a quadratic function modeling the height of a slide: $$f(x) = a(x - 5)^2$$ with initial height 2.5 m at $x=0$. We need to find the height of the strut positioned at $x=1$ m. 2. **Recall the formula:** The height at any horizontal distance $x$ is given by $$f(x) = a(x - 5)^2$$ where $a$ is a constant. 3. **Find $a$ using the initial height:** At $x=0$, the height is 2.5 m, so $$2.5 = a(0 - 5)^2 = a(25)$$ which gives $$a = \frac{2.5}{25} = 0.1$$ 4. **Calculate the height at $x=1$:** Substitute $x=1$ and $a=0.1$ into the function: $$f(1) = 0.1(1 - 5)^2 = 0.1( -4)^2 = 0.1 \times 16 = 1.6$$ 5. **Interpretation:** The height of the strut at 1 m horizontal distance is 1.6 m. **Final answer:** $$\boxed{1.6\text{ m}}$$