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Definition
| in geometry the movement of all of the poitnts of a gemetric figure according to a specific set of rules, creating a new geometric figure. This movement is often called a "mapping", and establishes a correspondence between the ponts of the original figure, and the poits of the new figure |
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| the original geometric shape before a transformation is applied to it. The pre-image is soemtimes called the object. |
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| the geometric shape which appears after a transformation has been applied to the pre image |
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| sometimes called a rigid transformation or a slide, this is a size and shape preserving transformation, which maps every point in teh pre-image, to its corresponding point in the image, by a set of straight line segments--all of which are parallel and equal in length, THis transformation is defined by teh direction and length of the movement, and is shown by a translation vector ( ) which shows the distance adn direction of the translation. |
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| this transformation rotates the pre-image about a fixed point, in such a way that every point in teh pre-image turns thorugh the same sized angle relative to that fixed point, preserving shape and size. A rotation is degined by the postiion fo the fiexed point about which the turn is made(called the center fo rotation), the direction (usually counter clockwise, and called the direction fo rotation), and the angle of the turn (called the angle fo rotation in degrees). It is shown by teh fixed point and a directional arc for a specific angle. |
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Definition
| a transformation in which each point of hte pre-image moves across a fixed line to a point in teh image, whichi si the same distance from that fixed line (called th eline of reflection or the mirror line) as th eoriginal point. A reflection is defined by teh line fo reflection, ans is shown by that line, with arrowheads on each end. This transformation also preserves shape and size. |
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| a transformation in which the distance between any point of the pre image and a specified point(called the center fo dialation), is multipleid by some constant factor to produce the image. A dilation is defined by that center fo dialation adn themultipler (called the scale factor), which will enlarge th epre image if the multiplier has an absolute value greatier than one, or reduc the image if hte multiplier has an absolute value strictly between zero and one |
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Definition
| a transformation or combination of transformations which results in te iamge being exactly the same shpae an dsize as the pre image |
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Term
| simsilarity transformation |
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Definition
| a transformation or comibation of tranformations wihch result in the image being exactily the shape shpae, but not the same size as the pre iamge |
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