Final answer:
The question deals with geometric transformation, specifically the 90° clockwise rotation of a triangle about a point, which is a key concept in geometry that applies to various scenarios such as rotations on a merry-go-round and differences in arc lengths due to the distance from the center of rotation.
Step-by-step explanation:
The student's question involves a geometric transformation, specifically the rotation of a triangle about a point. When ∆ABC rotates 90° clockwise around point P to form ∆A'B'C', we are dealing with a classical problem in geometry that involves understanding angles, shapes, and their movement in a plane. In such problems, the properties of the shapes are preserved, meaning the size and shape of the triangle remain the same, but its position and orientation change.
Understanding the concept of rotation is fundamental in geometry. For instance, in the context of rigid body rotation, when a body rotates through an angle from one point to another due to an external force applied at a point, the motion is described under the same principles. This concept is seen in various scenarios such as the merry-go-round described in Figure 6.15, where a ball follows a curved path due to the rotation of the platform.
It's important to grasp that the distance from the center of rotation matters as well. As illustrated in Figure 6.4, points that are further away from the rotation center travel through a longer arc, despite rotating through the same angle. This principle leads to different arc lengths for points at varying distances from the center.