Example Series: Dilation with scale factor 2, a reflection over the y-axis, a translation 6 units down, and a dilation with scale factor 12
Practice makes perfect
We are asked to describe a series of transformations where the image is congruent to the preimage. However, our series must contain at least one dilation. Let's consider an example figure.
Next, let's reflect the figure over the y-axis and then translate it 6 units down.
Notice that the image of our series of transformations is not congruent to the original figure because the sizes of the two figures are different. Specifically, each side of the image is 2 times longer than the corresponding side of the preimage.
The scale factor of a composition of two dilations is the product of the scale factors of the dilations. Therefore, to make the figures congruent, we will apply a dilation with center at the origin and scale factor equal to 12 as the final transformation in our series.
The image of our series of transformations is congruent to the preimage. A series of transformations, including at least one dilation, where the image is congruent to the preimage, is a dilation with scale factor equal to 2, a reflection over the y-axis, a translation 6 units down, and a dilation with scale factor 12.
This is just one example of an infinite number of series of transformations that meet the given criteria.
