So if I were to start, if I were to, let me draw some coordinate axes here. So let's just first thinkĪbout what a negative 270 degree rotation actually is. So actually let me go over here so I can actually draw on it. The points of this triangle around the origin by negative 270 degrees, where is it gonna put these points? And to help us think about that, I have copied and pasted So what we want to do is think about, well look, if we rotate And this tool, I can put points in, or I could delete points. So positive is counter-clockwise, which is a standard convention, and this is negative, so a negative degree would be clockwise. The direction of rotationīy a positive angle is counter-clockwise. So this is the triangle PINĪnd we're gonna rotate it negative 270 degrees about the origin. We're told that triangle PIN is rotated negative 270ĭegrees about the origin. I hope this gives you more of an intuitive sense. If you want, you can connect each vertex and rotated vertex to the origin to see if the angle is indeed 90 degrees. As per the definition of rotation, the angles APA', BPB', and CPC', or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees. The rotated triangle will be called triangle A'B'C'. The point at which we do the rotation, we'll call point P. Well, let's say the shape is a triangle with vertices A, B, and C, and we want to rotate it 90 degrees. The shape is being rotated! But how do we do this for a specific angle? ![]() With your finger firmly on that point, rotate the paper on top. Now place your finger on the rotation point. ![]() Put another paper on top of it (I like to imagine this one as being something like a transparent sheet protector, and I draw on it using a dry-erase marker) and trace the point/shape. Here's something that helps me visualize it: The "formula" for a rotation depends on the direction of the rotation. I'm sorry about the confusion with my original message above. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a) 180 = (-a, -b) 270 = (-b, a) 360 = (a, b). Also this is for a counterclockwise rotation. 360 degrees doesn't change since it is a full rotation or a full circle. ![]() 180 degrees and 360 degrees are also opposites of each other. So, (-b, a) is for 90 degrees and (b, -a) is for 270. Refer to About These Materials in the Geometry course for more information.The way that I remember it is that 90 degrees and 270 degrees are basically the opposite of each other. Students will continue adding to it throughout the course. Students then begin to use the rigorous definitions they developed to prove statements involving angles and distances, preparing them for congruence proofs in the next unit.Ī blank reference chart is provided for students, and a completed reference chart for teachers. The purpose of the reference chart is to be a resource for students to reference as they make formal arguments. In this unit, they transition to more formal definitions that don't rely on the coordinate plane, and the focus shifts from transforming whole figures towards a more point-by-point analysis. In middle school, students studied transformations of figures in the coordinate plane. This allows them to build conjectures and observations before formally defining rotations, reflections, and translations. In this unit, students first informally explore geometric properties using straightedge and compass constructions.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |