Question

complete the steps that describe the sequence of rotations, reflections, and dilations that show one figure is similar to the other.

1. start with figure bcde.
2. dilate using select choice as the center of dilation with scale factor select choice.
3. select choice using a as the center select choice 30 degrees.
4. select choice along the line that contains a and the image of e under the previous transformations.

(lesson 2 - 6)

Explanation:

Step1: Determine the center of dilation

The center of dilation is point \(A\) as it is the fixed point around which the figure is scaled.

Step2: Find the scale factor

By comparing the lengths of corresponding sides (e.g., if the length of a side in \(BCDE\) is \(2x\) and in \(B''C''D''E''\) is \(x\), the scale factor is \(\frac{1}{2}\)).

Step3: Rotation details

Rotate the dilated figure. The rotation is clock - wise (assuming the direction from the figure's orientation) around center \(A\) by \(30\) degrees.

Step4: Reflection details

Reflect the rotated figure along the line that contains \(A\) and the image of \(E\) (after dilation and rotation) to get the final similar figure.

Answer:

1. \(A\); \(\frac{1}{2}\) (assuming a typical side - length ratio). 3. Rotate; clock - wise. 4. Reflect.