Final answer:
The principle where the performance of the component's activity is crucial for system objectives is the Functional Principle. It emphasizes that design should be derived from the intended use, aligning with the 'form follows function' philosophy prevalent across many design fields.
Step-by-step explanation:
The term that relates to the principle in which the performance of the activity with the component is vital to the achievement of the objectives of the system is the Functional Principle. This principle is paramount in design, as it insists that the form of a building or structure should be primarily based on its intended function. This is consistent with the popular axiom 'form follows function', which applies not only in architecture but in various design disciplines, ensuring that the design of a product, building, or system facilitates the activity for which it was created.
When architects and designers are working on architectural drawings and city layouts, they integrate the functional principle by organizing elements according to the planned use of the space, with careful consideration for the flow and frequency of activities within the space. The design process, influenced by various principles such as sequence-of-use and frequency-of-use, ultimately emphasizes the function of achieving a balance between aesthetics and utility.