January 2nd, 2009, 04:57 AM
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 Translation
Hello nevetha
Quote:
Originally Posted by nevetha  Consider there is a polygon and a point P within the polygon. When the polygon is translated ( rotated or transformed to a new position or both) then the point should also be translated with respect to the new polygon position.
Can anyone figure it out. Thanks in advance  | I don't understand the question here. Can you re-phrase it?
In a translation, a polygon is moved to a new position in such a way that all points on the polygon move the same distance in the same direction, so that the new shape (the image) has exactly the same orientation as the original shape (the pre-image).
In a rotation, all points of the pre-image are rotated through the same angle about a fixed point - the centre of the rotation. Thus the polygon keeps its shape and size, but not its orientation (unless, of course, the angle of rotation is 360 degrees).
In a reflection, the lines joining corresponding points on the image and pre-image are parallel, and their mid-points lie on a straight line perpendicular to these lines. This is the 'mirror-line' of the reflection. The image is congruent to the pre-image but is opposite in 'sense'; in other words, if you move clockwise around the perimeter of the image, then you'll move anti-clockwise around corresponding points of the pre-image.
Rotations, translations and reflections (and any combination of them) are called isometries, because the image is congruent to the pre-image. But the word transformation may be used to denote other types of operation in which the image and pre-image are not congruent; e.g. stretching, shearing, etc.
So I think we need a bit more information about what is being asked here.
Grandad
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