If the polygons do not have the same side lengths, consider a dilation.
Example Solution: r_((180^(∘),O)) ∘ D_(1.5)
Practice makes perfect
We will describe the composition of transformations that map △FGH to △QRS.
The side lengths of △QRS are 1.5 the side lengths of △FGH. Moreover, without considering the lengths, △QRS seems to be a rotation of △FGH 180^(∘) about O. Therefore, △QRS appears to be the image of △FGH after a dilation by a scale factor of 1.5, followed by a rotation 180^(∘) about O. Let's confirm this!
Dilation
Let's dilate △FGH by a scale factor of 1.5 and center of dilation O(0,0). To do so, we will find the images of the vertices by multiplying their coordinates by the scale factor. Let F', G', and H' be their corresponding images. Therefore, D_(1.5) ( △FGH)= △F'G'H'.
Finally, we will rotate △F'G'H' by 180^(∘) about the origin O(0,0).
Composition
We can conclude that △QRS is the image of △FGH after a dilation by a scale factor of 1.5 and center O(0,0), followed by a rotation 180^(∘) about O(0,0).
( r_((180^(∘),O)) ∘ D_(1.5) ) ( △FGH) = △QRS
