The answer to which graph shows a dilation is not as simple as determining if there is a direct path from two points in the original figure. A dilation is a transformation that enlarges the size of a figure without changing its shape. This can be done by a factor of either a horizontal or vertical scale. Horizontal dilation squishes the function, while vertical dilation extends it.

When a function is dilated, the coordinates of all of its points are multiplied by the same value. As a result, the proportions of the original figure remain the same in the dilated image. For this reason, a square will not be transformed into a rectangle and a trapezoid will not transform into a rhombus.

In order to determine whether or not a particular graph shows a dilation, it is necessary to identify its key points and the location of the fixed point. The key points of a figure are the endpoints, vertices, and centers. The fixed point is the point that maps to itself in a transformation, and it may or may not be located on the figure itself.

A fixed point does not have to be at the center of the figure, but it can be at any other place on the plane. Once the key points and the fixed point have been identified, the next step is to find out which direction the shape will be dilated by. Horizontal dilation by a factor of 1 expands the function, while vertical dilation by a factor of 0 or a negative number stretches it.