1. The problem asks to write a rule describing the transformation shown in the first graph of a polygon and its image on a coordinate grid. 2. To describe a transformation, we identify how each point of the original figure moves to its image. Common transformations include translations, reflections, rotations, and dilations. 3. Observe the coordinates of corresponding vertices before and after the transformation. 4. Suppose the original polygon has a vertex at $(x,y)$ and its image is at $(x',y')$. 5. If the transformation is a translation, the rule is $T(x,y) = (x + a, y + b)$ where $a$ and $b$ are the horizontal and vertical shifts. 6. If the transformation is a reflection, the rule depends on the line of reflection, for example, reflection over the y-axis is $R(x,y) = (-x,y)$. 7. If the transformation is a rotation, the rule depends on the center and angle, for example, a 90° rotation about the origin is $R(x,y) = (-y,x)$. 8. If the transformation is a dilation, the rule is $D(x,y) = (kx, ky)$ where $k$ is the scale factor. 9. By comparing the coordinates of the polygon and its image, determine the values of $a$, $b$, $k$, or the nature of reflection or rotation. 10. Write the transformation rule accordingly. Since the exact coordinates and images are not provided, the general approach is to identify the type of transformation and write the corresponding rule as above.