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
[tex]k=\dfrac{\text{Side of image}}{\text{Corresponding side of original figure}}[/tex]
We know that, MNOP is the original figure and WXYZ is the image. MN is corresponding side of WX.
[tex]k=\dfrac{WX}{MN}[/tex] ...(i)
Each side of MNOP is 2 times as long as the corresponding side of WXYZ.
[tex]MN=2WX[/tex]
[tex]\dfrac{1}{2}=\dfrac{WX}{MN}[/tex]
[tex]0.5=\dfrac{WX}{MN}[/tex] ...(ii)
From (i) and (ii), we get
[tex]k=0.5[/tex]
Therefore, the correct option is B.
