Select the correct answer. Which sequence of transformations proves that shape I is similar to shape II?

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C. a reflection across the x-axis, and then a dilation by a scale factor of 2

Step-by-step 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

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step-by-step explanation: