Which series of transformations can be used to show that is similar to ?

Question

A.

a 90° clockwise rotation about followed by a dilation through by scale factor


B.

a reflection across a vertical line passing through followed by a dilation through by a scale factor of


C.

a reflection across a vertical line passing through followed by a dilation through by a scale factor of


D.

a 90° clockwise rotation about followed by a dilation through by scale factor

Answer 1

To determine which series of transformations can show that one shape (let's call it Shape A) is similar to another shape (Shape B), we need to analyze the types of transformations involved. Similar shapes can be obtained through rotations, reflections, and dilations.

1. Rotation: Rotating a shape around a point can change its orientation but preserves angles and therefore can lead to similarity.

2. Reflection: Reflecting a shape across a line allows for maintaining the shape's dimensions while altering its position.

3. Dilation: Scaling a shape by a certain factor enlarges or reduces its size, again preserving the shape's angles and leading to similarity.

Now, let's look at the options:

• A. A 90° clockwise rotation followed by a dilation with a scale factor. This transformation can change the orientation and size, likely leading to similarity.

• B. A reflection across a vertical line followed by a dilation with a scale factor. This could also produce a shape that is similar by changing position and then scaling.

• C. A reflection across a vertical line followed by a dilation with a scale factor. This is similar to option B and can also result in a similar shape.

• D. A 90° clockwise rotation followed by a dilation with a scale factor. This is identical to option A and thus likely results in similarity.

To summarize:

• Options A and D both involve a rotation and then dilation, suggesting they lead to similarity.
• Options B and C involve reflection followed by dilation, also indicating similarity.

In conclusion, without specific information about shapes and transformations, it seems that transformations involving a combination of rotation or reflection with dilation will likely demonstrate similarity. The specific answer would depend on the exact nature of shapes A and B, but all options could potentially lead to similarity of shapes provided the correct scale factors and conditions apply.

Please refer back to your analysis or a specific condition associated with the shapes to determine the exact suitable transformations.