Answer:
Scale factor 2.
Step-by-step explanation:
The vertices of shape I are (2,1), (3,1), (4,3), (3,3), (3,2), (2,2), (2,3), (1,3).
The vertices of shape II are (-4,-2), (-6,-2), (-8,-6), (-6,-6), (-6,-4), (-4,-4), (-4,-6), (-2,-6).
Consider shape I is similar to shape II. The sequence that maps shape I onto shape II is a 180 degree clockwise rotation about the origin, and then a dilation by a scale factor of k.
Rule of 180 degree clockwise rotation about the origin:
[tex](x,y)\rightarrow (-x,-y)[/tex]
The vertices of shape I after rotation are (-2,-1), (-3,-1), (-4,-3), (-3,-3), (-3,-2), (-2,-2), (-2,-3), (-1,-3).
Rule of dilation by a scale factor of k.
[tex](x,y)\rightarrow (kx,ky)[/tex]
So,
[tex](-2,-1)\rightarrow (k(-2),k(-1))=(-2k,-k)[/tex]
We know that, the image of (-2,-1) after dilation is (-4,-2). So,
[tex](-2k,-k)=(-4,-2)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2.
