![]() ![]() You can know how to slide a shape using the T ( a, b ) T ( − 10, 3 ) because the first value is always the x-axis. To avoid confusion, the new image is indicated with a little prime stroke, like this: P′, and that point is pronounced “ P prime. Suppose you have Point P located at (3, 4). The original reference point for any figure or shape is presented with its coordinates, using the x-axis and y-axis system, (x,y). As you'll see, the student must revise their definition several times to make it more and more precise. Their goal is to describe rotations in general using precise mathematical language. The dialog below is between a teacher and a student. Reflection – exchanging all points of a shape or figure with their mirror image across a given line (like looking in a mirror) Read a dialog where a student and a teacher work towards defining rotations as precisely as possible. Stretch – a one-way or two-way change using an invariant line and a scale factor (as if the shape were rubber) Shear – a movement of all the shape’s points in one direction except for points on a given line (like a crate being collapsed) 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. Dilations, on the other hand, change the size of a shape, but they preserve. ![]() Rigid transformationssuch as translations, rotations, and reflectionspreserve the lengths of segments, the measures of angles, and the areas of shapes. Rotation – turning the object around a given fixed pointĭilation – a decrease in scale (like a photocopy shrinkage)Įxpansion – an increase in scale (like a photocopy enlargement) So, (-b, a) is for 90 degrees and (b, -a) is for 270. We often use rigid transformations and dilations in geometric proofs because they preserve certain properties. Translation – moving the shape without any other change You can perform seven types of transformations on any shape or figure: Translations are the simplest transformation in geometry and are often the first step in performing other transformations on a figure or shape.įor example, you may find you want to translate and rotate a shape. an isometry) because it does not change the size or shape of the original figure. A translation is a rigid transformation (a.k.a. ![]()
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