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Learn about the importance of distinguishing between original figures and images in similar transformations. Explore how similar squares differ from congruent squares and the key concepts of dilations. Enhance your visualization skills with practical tips.
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Two figures are similar if one can be obtained from the other using a sequence of transformations in the plane.
Why is it important to know which figure is the original figure and which is the image?Knowing which is the original figure allows you to find the correct order of the transformations and the scale factor of the dilation.
How are similar squares different from congruent squares? Congruent squares have the same shape and size.Similar squares have the same shape but are not necessarily the same size.
Every dilation must be described by two pieces of information: the scale factor and the center of dilation. The distance from the center of dilation to each point of the image is equal to the distance from the center of dilation to each corresponding point of the original figure times the scale factor. If the center of dilation is at vertex A of the original figure, the corresponding vertex on the dilation image has the same coordinates as vertex A.
If you cannot visualize the sequence of transformations, use a paper cut-out that is the same size and shape as the image that you can rotate and translate on a coordinate grid. Once the shape is centered on the origin in the proper orientation, it is ready for the dilation.
How do you know when a dilation has occurred? The image is either larger or smaller than the original figure, and the original figure and image are similar.
