Question

Select the correct answer from each drop-down menu. Shape I is similar to shape II. The sequence that maps shape I onto shape II is a 180degree clockwise rotation about the origin, and then a dilation by a scale factor of (0.5; 1; 1.5 ; or 2)

Answer 1

Answer:

180 clockwise rotation about the orgin, 2

Step-by-step explanation:

Answer 2

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:

$(x,y)\rightarrow (-x,-y)$

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.

$(x,y)\rightarrow (kx,ky)$

So,

$(-2,-1)\rightarrow (k(-2),k(-1))=(-2k,-k)$

We know that, the image of (-2,-1) after dilation is (-4,-2). So,

$(-2k,-k)=(-4,-2)$

On comparing both sides, we get

$-2k=-4$

$k=2$

Therefore, the scale factor is 2.