Answer:
A scaled copy in mathematics refers to a figure or object that has been resized proportionally (either enlarged or reduced) while maintaining the same shape. Here are five facts about scaled copies:
Proportional Size Change: When creating a scaled copy, all corresponding lengths of the original figure and its copy are changed by the same scale factor. This means that if one side of the original figure is twice as long as another side, the corresponding side of the scaled copy will also be twice as long as its corresponding side.
Similar Figures: Scaled copies are always similar figures. Similar figures have the same shape but may differ in size. In other words, all corresponding angles of similar figures are congruent.
Scale Factor: The scale factor is the ratio by which the dimensions of the original figure are scaled to create the copy. If the scale factor is greater than 1, it results in an enlargement; if it's less than 1, it results in a reduction. For example, a scale factor of 2 means the figure is enlarged to twice its original size.
Area and Perimeter: When you create a scaled copy, the area of the copy is scaled by the square of the scale factor. The perimeter (or circumference for circles) is scaled by the scale factor. For example, if the scale factor is 2, the area of the copy will be 4 times the area of the original, and the perimeter will be 2 times the original.
Applications: Scaling plays a crucial role in various real-world applications. For instance, maps, architectural blueprints, and engineering designs often involve scaled copies to represent large objects or areas in a more manageable size. Scaled copies are also used in art, photography, and computer graphics to manipulate the size of images while preserving their proportions.