Question

write a coordinate rule for the composition (the blue preimage to the green image).

Explanation:

Step1: Find the translation rule

First, observe the coordinates of a point in the blue pre - image and its corresponding point in the green image. Let's assume a general point \((x,y)\) in the blue figure.
Looking at the horizontal (x - axis) and vertical (y - axis) movements.
For the x - coordinate:
If we consider the transformation from the blue figure to the green figure, we can see that the x - coordinate of each point in the blue figure is decreased by 4. That is, if the original x - coordinate is \(x\), the new x - coordinate is \(x-4\).
For the y - coordinate:
The y - coordinate of each point in the blue figure is decreased by 8. That is, if the original y - coordinate is \(y\), the new y - coordinate is \(y - 8\).

Answer:

\((x,y)\to(x - 4,y-8)\)