Answer:
C. a reflection across the x-axis, and then a dilation by a scale factor of 2
Explanation:
Transformations
If a given point (x,y) is reflected across the x-axis, it transforms to (x,-y).
If a given point (x,y) is rotated counterclockwise 90° about the origin, it transforms to (-y,x)
If a given point (x,y) is dilated by a factor scale of k, it transforms to (kx, ky).
We are given a shape called Image I formed by the points:
(4,-1) (6,-3) (3,-3) (3,-2)
The shape called Image II is formed by the points:
(8,2) (12,6) (6,6) (6,4)
Let's take the first point of Image I (4,-1).
A reflection across the x-axis will make it (4,1). A dilation by 2 will make it (8,2) which coincides with the first point of Image II.
Let's take the point (6,-3) of Image I.
A reflection across the x-axis will make it (6,3). A dilation by 2 will make it (12,6) which coincides with the second point of Image II.
Let's take the point (3,-3) of Image I.
A reflection across the x-axis will make it (3,3). A dilation by 2 will make it (6,6) which coincides with the third point of Image II.
Let's take the point (3,-2) of Image I.
A reflection across the x-axis will make it (3,2). A dilation by 2 will make it (6,4) which coincides with the fourth point of Image II.
Thus, both shapes are similar because of the following sequence of transformations:
C. a reflection across the x-axis, and then a dilation by a scale factor of 2