Final answer:
The question involves transformations such as rotations and reflections within the cartesian coordinate system in geometry, as well as the reflection of light based on the law of reflection in optics.
Step-by-step explanation:
The discussion encompasses topics from geometry, specifically transformations in the coordinate plane and reflection properties. Rotating a point 180° about the origin changes its coordinates from (x, y) to (-x, -y). A subsequent reflection in the y-axis transforms it to (x, -y), equivalent to reflecting the original point across the x-axis. These operations illustrate concepts in the transformation of coordinates, a fundamental part of geometry.
Reflections based on the law of reflection and properties of cartesian coordinates are used in various applications, including optics and vector analysis. In optics, the law of reflection dictates that the angle of incidence equals the angle of reflection, affecting the path of light rays and the formation of images by mirrors. In a cartesian plane, reflections over the x or y-axis result in specific sign changes to the coordinates of points.
The use of vectors and their properties, such as invariance under rotation of the coordinate system, is integral to understanding how objects and points behave in a plane and space. The coordinate system can also be extended into three dimensions using an additional z-coordinate, enhancing the application of these concepts beyond two-dimensional transformations.