Question

Select the correct answer.

The image of polygon MNOP after a similarity transformation is polygon WXYZ. Each side of MNOP is 2 times as long as the corresponding side
of WXYZ. What is the scale factor of the dilation in the similarity transformation?
OA 4
OB 0.5
Ос. 2
OD. 0.25
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mii

Answer 1

Given:

The image of polygon MNOP after a similarity transformation is WXYZ.

Each side of MNOP is 2 times as long as the corresponding side of WXYZ.

To find:

The scale factor of the dilation in the similarity transformation.

Solution:

We know that, the scale factor is

`k=\frac{\text{Side of image}}{\text{Corresponding side of original figure}}`

We know that, MNOP is the original figure and WXYZ is the image. MN is corresponding side of WX.

`k=(WX)/(MN)` ...(i)

Each side of MNOP is 2 times as long as the corresponding side of WXYZ.

`MN=2WX`

`(1)/(2)=(WX)/(MN)`

`0.5=(WX)/(MN)` ...(ii)

From (i) and (ii), we get

`k=0.5`

Therefore, the correct option is B.