Answer:
The composition of similarity transformations are:
a dilation with a scale factor less than 1 and then a reflection
Step-by-step explanation:
Polygon ABCD is dilated or transformed to polygon A'B'C'D' by some scale factor.
Clearly as the image is a shrink as compared to the pre-image.
Hence, there is a dilation with the scale factor less than 1.
Also the coordinated of D are (0,-4).
and the coordinates of D' are (0,-2).
so let k be a scale factor of the dilation.
i.e. (x,y) → (kx,ky)
Let the coordinates of D are treated as (x,y) and that of D' are considered as (kx,ky).
Hence, (x,y)=(0,-4)
and (kx,ky)=(0,-2)
(k×0,k×4)=(0,-2)
i.e. -4k=-2
⇒ k=1\2.
Hence the scale factor is: 1/2 which is less than 1.
Also the graph is then reflected across the y-axis.
Hence option A is correct.
a dilation with a scale factor less than 1 and then a reflection.
