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In geometry, one type of transformation is called a dilation. A dilation maps a point P in the plane to a point P'(called the image) where P' lies on the ray from O(the center of the dilation) through P; the distance from O to P' is k (the dilation or scale factor) times the distance from O to P. (If k<0, P' is mapped on the ray opposite of OP)
Dilations map figures to similar figures. Similar figures have the same shape (parallel lines are mapped to parallel lines, angles are mapped to congruent angles) but not necessarily the same size. The lengths of line segments will be in a set proportion to their preimages (the segments of the original figure.)
To define a dilation we determine a center and the scaling factor. The scale factor is a constant ratio comparing lengths of the preimage to the image. That is, if the scale factor is 1:2 ( or 1/2), the image or projection has segments 1/2 as long as the original.
You have probably used this yourself -- when using a copier or photo enhancement package if you resize the original you are applying a dilation. If you select to reduce to 90%, this is a scale factor of 9/10. If you resize to 120% the scale factor is 6/5.
Blueprints and other schematics use scale diagrams. The original sizes are scaled to fit on the paper. The scale gives you a way to convert the image sizes (on the paper) to the original sizes. If the scale is 1":12', anything on the diagram that is 1.5" long represents an object 18' long. This type of ratio is also applied with model cars and train sets.
Scale diagrams help us to draw very large things in real life, in a smaller diagram or a smaller real life thing in a much larger way. It helps us to get our whatever work done using the ratios that we used in our scale diagrams. We use these ratios so that we can make them large or small exactly as to the real thing. If we want to find may be a resultant distance those exact ratio values will help us find the original resultant after the conversion using the ratio that we initially stated, decided and used in our diagram.
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