Flips, Reflections, Rotation, and Quadrants
Date: 11/10/98 at 23:52:30 From: Roger Johnson Subject: Quadrants, reflections, flips, and rotation My daughter is in fifth grade. These terms are being used to describe the movement of shapes. I have no idea what they are talking about and neither does she. Any ideas? Roger L. Johnson
Date: 11/11/98 at 08:53:56 From: Doctor Rick Subject: Re: Quadrants, reflections, flips, and rotation Hi, Roger. Do you have a computer drawing program? These terms, except perhaps for "quadrant," can probably all be found there, and this could be a good way to gain an understanding of the concepts. In many drawing programs, you can create a shape with something like a "polygon tool." Then, while the shape is selected, you can go to a menu and find commands "flip," "reflect," and "rotate." Some programs might use different terms, and not every program can do free rotation, so I'll describe them. "Flip" is a (not very technical) term for switching the top and bottom of a figure. Imagine attaching a horizontal rod across the middle of the shape, then rotating the figure half a turn about the rod. The top is now on the bottom and the bottom is now on the top. "Reflect" refers to what you see when you look in mirror: your left hand becomes the right hand of the reflection, and your right hand becomes its left hand. So we often use the word "reflect" to mean the same thing as "flip" except that the imaginary rod on which you turn the shape is vertical this time rather than horizontal. In more technical use, a "reflection" can be about any axis, horizontal or vertical or at any angle. "Rotate" simply means to turn the shape, just as if you drew the shape on paper, put the paper on the desk, and turned the paper. "Quadrant" is a term that helps us describe where the parts of a shape are. If you draw horizontal and vertical lines, they divide the page into four parts, each called a quadrant. We number the quadrants like this: | | II | I | | ----------+----------- | | III | IV | | "Flipping" switches quadrant I with quadrant IV and switches quadrant II with quadrant III. "Reflecting" switches quadrant I with II and IV with III. Rotation clockwise by 90 degrees moves quadrant I to IV, II to I, III to II, and IV to III. Rotation counterclockwise by 90 degrees moves quadrant I to II, II to III, III to IV, and IV to I. Rotation by 180 degrees (either way) switches quadrant I with III and II with IV. Everything I've said is about two-dimensional shapes (shapes you can draw on paper). My description of reflection is wrong in 3 dimensions: it isn't rotation on an axis as I described it, but reflection in a plane (like a mirror). In two dimensions, these two actions are the same. I hope this has helped. If you have a drawing program that has these functions, it will be a big help to your daughter - but you can do the same things by just cutting a paper shape and turning and flipping it. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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