Final answer:
The new coordinates of a quadrilateral after a dilation of factor 1/2 are obtained by halving each of the x and y coordinates of the original vertices. Assuming the original vertices are (3, 2), (6, 4), and (16, 0), then the new vertices would be (1.5, 1), (3, 2), and (8, 0) respectively.
Step-by-step explanation:
The question asks about the new vertices of a quadrilateral after it has been dilated by a factor of 1/2. However, there seems to be a typo in the question as it also mentions a triangle. Assuming we're talking about a quadrilateral and given the original vertices as (a), (b), (c), and (d), after the dilation the new vertices should be half the distance from the origin, which would mean multiplying each coordinate of the original vertices by the dilation factor of 1/2. Therefore, each original vertex (x, y) would become (1/2 * x, 1/2 * y).
If we have an original quadrilateral with vertices at (3, 2), (6, 4), (16, 0) respectively, the new vertices would be:
- (1.5, 1) for vertex (a) - (3, 2)
- (3, 2) for vertex (b) - (6, 4)
- (8, 0) for vertex (d) - (16, 0)
Note that we do not have the coordinates for the fourth vertex of the quadrilateral, so it cannot be dilated. Also, one should ensure the presence of a typo regarding the change from quadrilateral to triangle in the student's question.