To determine which ordered pair is one of the pre-image vertices for the given image and scale factor, we need to consider that the center of the pre-image is the origin (0,0). Given this information, let's verify the potential pre-image vertices.
We are provided with four ordered pairs:
1. [tex]\((\frac{3}{5}, 1)\)[/tex]
2. [tex]\((\frac{5}{3}, 1)\)[/tex]
3. [tex]\((1, 1)\)[/tex]
4. [tex]\((5, 1)\)[/tex]
The image of a point under scaling can be determined by multiplying the coordinates by the scale factor. However, since the exact scale factor is not provided in the problem, we consider the given set of possible pre-image vertices directly.
Based on the answer:
- [tex]\((0.6, 1)\)[/tex] corresponds to [tex]\((\frac{3}{5}, 1)\)[/tex]
- [tex]\((1.6666666666666667, 1)\)[/tex] corresponds to [tex]\((\frac{5}{3}, 1)\)[/tex]
- [tex]\((1, 1)\)[/tex] is directly listed
- [tex]\((5, 1)\)[/tex] is directly listed
Each of these pre-image vertices is a feasible answer, depending on the scale factor applied, which transforms them precisely into the points mentioned in the image.
Conclusively, all four given ordered pairs [tex]\(\left(\frac{3}{5}, 1\right)\)[/tex], [tex]\(\left(\frac{5}{3}, 1\right)\)[/tex], (1, 1), and (5, 1) are potential pre-image vertices. Thus, any of them could be correct under appropriate conditions and scale factors.
