While they move, they retain their shape, otherwise the game wouldn't work as intended. The only slight difference here is that your character may have a slightly different sprite while jumping, but that can be ignored for the sake of visualizing the translations. The rotations are shown in this level by the saws. While the saws move up and down on their tracks, they rotate along their center, showing the player that they will in fact cut you up if you land on them.
Each time your character moves right or left, they will always face the direction they are moving. In the above picture, let's say you notice that you're going to hit the saw, so you choose to start moving back towards the platform that you jumped from. Your character flips horizontally so they are facing the direction they are moving, while still staying the same exact size and the same position they were in before moving.
All of these types of motions occur without changing the shape of the object or figure being moved. A rigid motion is a transformation of the plane that "preserves distance". Intuitively, you can think of rigid motions as the results of "movements" that preserve the shapes and sizes of objects. A reflection is basically the result of "flipping".
For example, when you turn a page in a book flat on a desk , you are essentially reflecting the page over the spine of the book. But the intuition for reflection as a "movement" is still there—the "shape" of the page should certainly stay the same. Food for thought: by this definition, the reflection you see in your mirror should also be a "flip", right? But a "flip" through what? Caveat: We won't actually "prove" that these are rigid motions, because it's hard to do so without defining all of geometry in terms of coordinates.
But Matt and I think they're more satisfying "assumptions" than Euclid's postulates. Suppose we have some figure drawn on an infinite two-dimensional transparent piece of paper. Let's cut the figure out using a pair of scissors. We can move the cut-out figure around on the paper—these movements are called transformations.
Now we can slide the figure around on the piece of paper. The figure itself looks the same, but now it's on a different part of the paper than it was before. Intuitive arguments with pictures can also be used and sample pictures are also provided in the solution. If the teacher desires a more open ended version of this task, part d can be used on its own.
A thorough study of fixed points can help provide a classification of rigid motions of the plane. With some more work it is possible to classify these cases as follows:. This line of reasoning extends part d of the task. Although it goes beyond the high school curriculum, this could make for a nice project in an advanced geometry class.
From each vertex, draw a line segment perpendicular to line l and make sure its midpoint lies on line l. Now draw the new positions of the vertices, making the transformed figure a mirror image of the original figure. The final transformation rigid motion that we will study is a glide-reflection, which is simply a combination of two of the other rigid motions. A glide-reflection is a combination of a reflection and a translation. First slide the smiley face two units to the right along the vector.
Then reflect the smiley face across line l. The final result is the green upside-down smiley face. First, slide the triangle along vector. Then, reflect the triangle across line l.
The final result is the green triangle below line l. First slide the L-shape along vector. Then reflect the L-shape across line l. The result is the green open shape below the line l. We could talk until we're blue in the face about this quiz on words for the color "blue," but we think you should take the quiz and find out if you're a whiz at these colorful terms. Words nearby rigid motion rigid designator , rigid frame , rigidify , rigidity , rigidize , rigid motion , Rigil Kent , Rigil Kentaurus , rigmarole , rigolet , Rigoletto.
How to use rigid motion in a sentence I wonder what that lady is doing now, and if she knows what she set in motion with Archer? Ramona Helen Hunt Jackson.
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