In a dilation transformation, every point in a figure is moved away from or toward a fixed point known as the center of dilation. The amount of movement is determined by a scale factor. In this case, the scale factor is 1, which indicates that each point will remain in its original position, as there is no scaling effect.
If we take a point g located at coordinates (x, y), applying a dilation with a scale factor of 1 will produce the image of point g at the same coordinates (x, y). Therefore, the image of g remains unchanged.
To summarize, for a dilation centered at (0, 0) with a scale factor of 1, the image of any point, including g, is simply the original point itself. This means that the dilation does not alter the position or the coordinates of point g.