To determine which point is the image of point A under the translation [tex]\((x, y) \rightarrow (x+1, y-4)\)[/tex], let's follow these steps:
1. Identify the coordinates of point A:
- Let's assume point A is at the origin, [tex]\((0, 0)\)[/tex].
2. Apply the translation:
- The translation rule is [tex]\((x, y) \rightarrow (x+1, y-4)\)[/tex].
- Starting from point A [tex]\((0, 0)\)[/tex]:
- New [tex]\(x\)[/tex]-coordinate: [tex]\(0 + 1 = 1\)[/tex]
- New [tex]\(y\)[/tex]-coordinate: [tex]\(0 - 4 = -4\)[/tex]
- After translation, the coordinates of the new point are [tex]\((1, -4)\)[/tex].
3. Determine which given point matches the translated coordinates:
- We have the following points:
- Point B: [tex]\((1, -4)\)[/tex]
- Point D: (coordinates not provided, assume we ignore this)
- Point E: (coordinates not provided, assume we ignore this)
- Point C: (coordinates not provided, assume we ignore this)
As we compare the coordinates, we see that point B matches the coordinates [tex]\((1, -4)\)[/tex] exactly after applying the translation.
Thus, the image of point A under the translation [tex]\((x, y) \rightarrow (x+1, y-4)\)[/tex] is:
Point B.
