Which composition of similarity transformations maps polygon abcd to polygon a'b'c'd'? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation

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.

the answer is two. hope this !