Final answer:
The equation describes a reduction dilation with a scale factor of 1/3. It's a geometric transformation shrinking the original figure towards the center of dilation.
Step-by-step explanation:
The equation D(x, y) = (1/3x, 1/3y) describes a type of geometric transformation known as dilation. In this case, the dilation has a scale factor of 1/3, which means that it is a reduction because the scale factor is less than 1. Every point of a shape is moved along a straight line away from or towards a fixed point, known as the center of dilation, to a distance determined by the scale factor.
For example, if you have a point (6,9) and you apply the dilation described by the given equation, the new coordinates would be (1/3 * 6, 1/3 * 9) = (2,3). This represents a shrunken version of the original figure.
The equation given describes a dilation where the x and y coordinates of each point are multiplied by a scale factor of 1/3. This type of dilation is called a scale factor dilation. When the scale factor is less than 1, like in this case, the dilation results in a reduction in size. For example, if a point is originally located at (3, 6), after the dilation it will be located at (1, 2). Each coordinate is multiplied by 1/3.