explain what relation a dilated figure has to its original
When a figure is dilated, it undergoes a transformation that changes its size while maintaining its overall shape and proportions. The dilated figure is an enlargement or reduction of the original figure, and it is related to the original figure in the following ways:
1. Similarity: The dilated figure is similar to the original figure, which means that corresponding angles of the two figures are congruent, and corresponding sides are in proportion or have the same ratio. The overall shape of the dilated figure is the same as the original, but it may be larger or smaller.
2. Center of dilation: The dilated figure is created by performing the dilation with respect to a center point, known as the center of dilation. The center of dilation is a fixed point through which all points of the original figure are expanded or contracted.
3. Scale factor: The relationship between the original figure and the dilated figure is determined by a scale factor. The scale factor represents the ratio of the corresponding lengths of the sides of the dilated figure to the original figure. If the scale factor is greater than 1, the dilated figure is an enlargement, and if it is between 0 and 1, it is a reduction.
4. Proportional measurements: The measurements of the dilated figure, such as side lengths, perimeters, and areas, are proportional to the measurements of the original figure. If the scale factor is 2, for example, the lengths of the sides in the dilated figure will be twice as long as the corresponding sides in the original figure.
In conclusion, the dilated figure retains the same shape as the original, while undergoing a change in size and maintaining proportional relationships. The original figure acts as a reference point, providing information about the dilation and serving as the basis for comparison.