Question

building on the essential question what is the difference between rotating a figure about a given point that is a vertex and rotating the same figure about the origin if the rotation is less than 360°?

Explanation:

When rotating a figure about a vertex, that vertex remains fixed and the other points move around it. When rotating about the origin, all points of the figure move relative to the origin. The position of the fixed - point (vertex vs. origin) affects the coordinates of the resulting rotated figure.

Answer:

When rotating about a vertex, one point of the figure remains stationary (the vertex itself), while when rotating about the origin, the origin is the fixed - point and all points of the figure move in relation to it. This leads to different sets of coordinates for the rotated figure in each case.