Final answer:
To dilate the quadrilateral by a factor of 1/2, multiply each coordinate of the vertices by 1/2. This results in new vertices at (1.5, 1), (3, 2), (6, 4), and (8, 0). Unrelated details in the question were disregarded.
Step-by-step explanation:
The student's question seems to involve a misunderstanding about dilations and the information provided has various unrelated facts that do not directly answer the question. To perform a dilation by a factor of 1/2, you would multiply each coordinate of the original quadrilateral's vertices by 1/2. However, the question mistakenly refers to a triangle instead of a quadrilateral and provides original vertices, but it is clear that the actual task is to shrink the size of a quadrilateral, which is a four-sided figure, not a triangle.
Applying the dilation factor of 1/2 to each vertex:
- For vertex a (3, 2), the new coordinates would be (1.5, 1)
- For vertex b (6, 4), the new coordinates would be (3, 2)
- For vertex c (12, 8), the new coordinates would be (6, 4)
- For vertex d (16, 0), the new coordinates would be (8, 0)
In each case, we simply take the original x and y values and multiply them by 1/2 to find the new, dilated vertex coordinates.
There seems to be mention of area calculations, velocity changes, and scale factors in different contexts which are not related to the specific task of performing a dilation on a quadrilateral. These should be disregarded for this particular problem.