Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
7. Similarity Transformations
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Exercise 10 Page 598

If the polygons do not have the same side lengths, consider a dilation.

R_(y-axis) ∘ 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 reflection of △FGH 90^(∘) across the y-axis. Therefore, △QRS appears to be the image of △FGH after a dilation by a scale factor of 1.5, followed by a reflection across the y-axis. 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'.

△FGH △F'G'H'
F(- 2,2) F'(- 2 * 1.5, 2* 1.5) ⇒ F'(- 3,3)
G(- 1,- 2) G'( - 1 * 1.5, - 2* 1.5) ⇒ G'(- 1.5,- 3)
H(0,- 1) H'(0* 1.5, - 1* 1.5) ⇒ H'(0,- 1.5)
Let's now perform the dilation on the coordinate plane.

Reflection

Finally, we will reflect △F'G'H' across the y-axis.

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 reflection across the y-axis. ( R_(y-axis) ∘ D_(1.5) ) ( △FGH) = △QRS