1. The problem asks for the scalar factor given that the image length $A'$ is 15 units. 2. The scalar factor (scale factor) is the ratio of the image length to the original length. 3. If the original length is $A$ and the image length is $A'$, then the scalar factor $k$ is given by: $$k = \frac{A'}{A}$$ 4. Since $A'$ is 15 units, we need the original length $A$ to find $k$. 5. Without the original length $A$, we cannot calculate the scalar factor. 6. Please provide the original length $A$ to proceed with the calculation.