1. The problem is to understand how the vector DE is calculated given that $x = (2,0)$ and $DE = \frac{3}{2} x$. 2. The formula used here is scalar multiplication of a vector: multiplying a vector by a scalar means multiplying each component of the vector by that scalar. 3. Given $x = (2,0)$, multiplying by $\frac{3}{2}$ means: $$DE = \frac{3}{2} \times (2,0) = \left( \frac{3}{2} \times 2, \frac{3}{2} \times 0 \right)$$ 4. Calculate each component: $$\frac{3}{2} \times 2 = 3$$ $$\frac{3}{2} \times 0 = 0$$ 5. So, the vector $DE$ is: $$DE = (3, 0)$$ 6. The step where you wrote $DE = (3/0)$ is a misunderstanding; it should be $(3,0)$, meaning the first component is 3 and the second component is 0, not a division. 7. In summary, scalar multiplication applies the scalar to each component individually, not as a division between components.