The four most common reflections are performed over the following lines of reflection: the $x$-axis, the $y$-axis, $y =x$, and $y =-x$. However, the orientation of the points or vertices changes when reflecting an object over a line of reflection. In fact, in reflection, the angle measures of the objects, parallelism, and side lengths will remain intact. The distances between the vertices of the triangles from the line of reflection will always be the same. The graph above showcases how a pre-image, $\Delta ABC$, is reflected over the horizontal line of reflection $y = 4$. ![]() This makes reflection a rigid transformation. When learning about point and triangle reflection, it has been established that when reflecting a pre-image, the resulting image changes position but retains its shape and size. This is also called an isometry, rigid transformations, or. In reflection, the position of the points or object changes with reference to the line of reflection. A rigid motion is that that preserves the distances while undergoing a motion in the plane. Once we’ve established their foundations, it will be easier to work on more complex examples of rigid transformations. We’ll explore different examples of reflection, translation and rotation as rigid transformations. It’s time to explore these three examples of basic rigid transformations first. This makes this transformation a rigid transformation.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |