Question

describe a similarity transformation that maps the black preimage to the dashed image

Explanation:

Step1: Analyze the transformation type

First, observe the position of the pre - image and the image. We can see that the pre - image is rotated and then dilated.

Step2: Determine the rotation

The pre - image is rotated \(180^{\circ}\) about the origin. For a point \((x,y)\) rotated \(180^{\circ}\) about the origin, the transformation rule is \((x,y)\to(-x,-y)\).

Step3: Determine the dilation

After rotation, we can see that the distance from the origin to the points of the image is twice the distance from the origin to the corresponding points of the rotated pre - image. The dilation factor \(k = 2\). The dilation rule is \((x,y)\to(kx,ky)\)

Answer:

A rotation of \(180^{\circ}\) about the origin followed by a dilation with a scale factor of \(2\) maps the black pre - image to the dashed image.