Question

select the correct figure.
the preimage undergoes the sequence of transformations to produce an image, figure 1

1. reflection across a horizontal line
2. rotation ( 30 ^ { circ } ) counterclockwise about point p
3. dilation with a scale factor of 1

which is the preimage?

Explanation:

Step1: Analyze the dilation

Since the scale factor of dilation is \(1\), the size of the pre - image and the image is the same.

Step2: Analyze the rotation

A \(30^{\circ}\) counter - clockwise rotation about point \(P\). If we reverse the rotation (i.e., rotate \(30^{\circ}\) clockwise about point \(P\) on figure 1) and then reverse the reflection (reflect back across the horizontal line), we can find the pre - image.
When we consider the orientation and position changes due to rotation and reflection:

• Reflection across a horizontal line changes the vertical orientation.
• Rotation changes the angular orientation.

By visual inspection and considering the inverse of the transformation sequence (first inverse rotation then inverse reflection) on figure 1, we can match the shapes.

Answer:

The pre - image is the figure on the left.