Final answer:
The Zhou Family believed they maintained the Mandate of Heaven, an ideological cornerstone that legitimized their rule and suggested that divine favor granted them the right to govern.
Step-by-step explanation:
The correct answer to the student's question is: The Zhou Family wasn't strong, and they thought they still had the Mandate of Heaven. The Zhou dynasty's concept of the Mandate of Heaven was integral to their ideological claim to rule after their victory over the Shang dynasty. This mandate was based on the understanding that heaven granted and revoked the right to govern based on the virtue and moral leadership of the ruling family. Misfortunes such as natural disasters and social tumult were regarded as indicators that a family's right to rule was in jeopardy. The family in question believed in the mandate to justify their rule, and it was used throughout Chinese history by various dynasties as a legitimizing principle.