Final answer:
To find the pre-image of vertex V under the dilation rule D(0.113)(x, y) = (14, 34), reverse the dilation process by dividing the image coordinates by the scale factor. Considering the scale factor and the provided options, the coordinates of vertex V of the pre-image are (0,3).
Step-by-step explanation:
The student is asking how to find the coordinates of vertex V given a dilation with a center at the origin and a scale factor. The rule given is D(0.113)(x, y) = (14, 34), which means a dilation by a scale factor of 0.113 results in the point (x, y) being transformed to (14, 34). To find the pre-image of vertex V, we effectively need to reverse the dilation process.
Using the rule for reverse dilation, which is to divide the coordinates of the image by the scale factor, we have:
Original x-coordinate = Image x-coordinate / Scale factor
Original y-coordinate = Image y-coordinate / Scale factor
For vertex V, this gives us:
x = 14 / 0.113
y = 34 / 0.113
However, the possible answers suggest that the original coordinates for vertex V must have been whole numbers. Since the scale factor is 0.113, the only provided option that, when multiplied by 0.113, would give a whole number close to 14 for x and 34 for y is option D) (0,3). Therefore, the coordinates of vertex V of the pre-image are (0,3).