What is translation?
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This document discusses translations in geometry. It provides examples of translating rectangles by moving them to new positions on a Cartesian plane. Translations only involve moving the figure and do not change its size or shape. The key elements of a translation are that there is a pre-image figure which is moved to create the image figure. Translations specify how far and in what direction each point of a figure moves.
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Unit 1. day 2
1) A translation "slides" each point of a figure the same distance in the same direction, shifting the figure without changing its size or shape.
2) Translating a polygon results in a congruent figure, with corresponding vertices having the same coordinates but shifted by the translation amount.
3) The order of multiple translations does not change the final result.
Unit 1. day 6
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This document discusses different types of transformations in mathematics. It defines a transformation as a change in position or orientation of a figure that results in an image of the original. Translations move a figure along a straight line without turning. Reflections flip a figure across a line. Rotations turn a figure around a point. Dilations change the size of a figure. The document provides examples of identifying transformations and graphing translations and reflections on a coordinate plane.
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2) Translations (slides) move every point of a figure by the same displacement vector, resulting in a figure pointing in the same direction. Reflections (flips) produce an image with the opposite orientation across a mirror line.
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This document discusses various types of transformations in mathematics including reflections, translations, rotations, and patterns formed from them. It defines transformations of the plane as one-to-one correspondences between points that map an original figure onto its image. Rigid motions are defined as transformations that preserve distances between points. Reflections flip figures across an axis, translations slide figures in a direction, and rotations turn figures around a center point. Patterns in nature often use these transformations and polygons and polyhedra can be found throughout the environment.
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A geometric transformation changes a geometric shape in some way. There are several types of transformations including translations, rotations, reflections, dilations, and glide reflections. Translations move a shape without changing it. Rotations turn a shape about a point. Reflections flip a shape across a line. Dilation enlarges or shrinks a shape uniformly. Glide reflections involve reflecting a shape and translating it. Common transformations are Euclidean transformations of translation, rotation, and reflection. Affine transformations preserve points, lines, and planes while projective transformations send geometric elements to elements of the same kind.
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What is translation?
- 2. Look at this image… What do you notice? Yes! They moved. Now they have changed their positions.
- 3. This movement is called translation. Let’s see another example of translation. Answer: Are there any change in size? Shape? Or anything else? You are right! There are no changes, It is just about moving the same figure!
- 4. Look at the distance of each vertex from the blue to red rectangle… What do you notice? Look at this translation. The blue rectangle was translated to the position showed by the red rectangle. Yes! The distance of each vertex is the same and also all of them are in the same direction.
- 5. LET’S LEARN WHAT THE ELEMENTS OF A TRANSLATION ARE 1. There is always a pre-image and an image. The pre-image is the original or initial figure. The blue square is the pre-image in this translation. The image is the figure after translation. The red square is the image in this translation.
- 6. 2. Translations are placed on Cartesian planes. A cartesian Plane helps us move easily a figure using the units it has.
- 7. CAN I TRANSLATE A FIGURE BY MYSELF? Of course you can. But how? Just move each point of the figure. 1. Follow the instruction. Example: Move the point 3 units to the right and 4 upwards. Great! We translated the point.
- 8. Thanks for your attention. Now… Let’s translate figures!