Figure undergoes a sequence of transformation that include dilutions. The figure and its final image are congruent explain how.
Only a dilation would change the shape's dimensions-- any type of shift would simply relocate the shape. We must only prove that dilation do not change the concurrency. Dilations, by definition scale on object-- if you dilate it by 2, the second image will be exactly twice the original. This is true for any legal dilation.
To understand how dilutions result in congruent images, let's first clarify what a dilution is. In mathematics, a dilution refers to the process of scaling or enlarging an object while maintaining its shape and proportions. When we dilute a figure, we uniformly change the size of the figure, but the shape of the figure remains the same.
Now, imagine that we have a figure and we dilute it by a scale factor of k. This means that every point of the original figure moves proportionally away from or towards the center of dilation by a factor of k. The resulting figure is similar to the original figure, but larger or smaller depending on the scale factor.
When a figure is dilated, it undergoes a transformation called a similarity transformation. Similarity transformations preserve shape, so the dilated figure will be congruent to the original figure. In other words, the dilated figure and the original figure have the same shape and thus can be superimposed perfectly without any rotations or reflections needed.
To verify that the final image after a sequence of dilutions is congruent to the original figure, you need to ensure that each dilution involved the same scale factor applied uniformly to all parts of the figure. As long as the dilutions meet these conditions, the resulting figure will always be congruent to the initial figure.