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Which of the following completes the rule for this translation, [tex]$(x, y) \rightarrow (x-8, \quad y \qquad J)$[/tex]?

A. [tex]y-6[/tex]

B. [tex]y-3[/tex]

C. [tex]y+6[/tex]

D. [tex]y+3[/tex]

Sagot :

GinnyAnsweridn
To determine the appropriate translation rule for the y-coordinate corresponding to the given translation rule for the x-coordinate, let's analyze each option systematically.

Given:
The translation rule for the x-coordinate is [tex]\((x, y) \rightarrow (x - 8, \quad J)\)[/tex]. We need to find the correct translation rule for the y-coordinate denoted by [tex]\(J\)[/tex].

Options for [tex]\(J\)[/tex] (the y-translation rule):
1. [tex]\( y - 6 \)[/tex]
2. [tex]\( y - 3 \)[/tex]
3. [tex]\( y + 6 \)[/tex]
4. [tex]\( y + 3 \)[/tex]

To evaluate which one completes the translation rule correctly, let's consider the possible scenarios:

1. Option [tex]\(y - 6\)[/tex]:
- If the translation rule is [tex]\((x, y) \rightarrow (x - 8, y - 6)\)[/tex], it implies that every point [tex]\( (x, y) \)[/tex] is translated to [tex]\( (x - 8) \)[/tex] in the x-direction and [tex]\( (y - 6) \)[/tex] in the y-direction.

2. Option [tex]\(y - 3\)[/tex]:
- If the translation rule is [tex]\((x, y) \rightarrow (x - 8, y - 3)\)[/tex], it implies that every point [tex]\( (x, y) \)[/tex] is translated to [tex]\( (x - 8) \)[/tex] in the x-direction and [tex]\( (y - 3) \)[/tex] in the y-direction.

3. Option [tex]\(y + 6\)[/tex]:
- If the translation rule is [tex]\((x, y) \rightarrow (x - 8, y + 6)\)[/tex], it implies that every point [tex]\( (x, y) \)[/tex] is translated to [tex]\( (x - 8) \)[/tex] in the x-direction and [tex]\( (y + 6) \)[/tex] in the y-direction.

4. Option [tex]\(y + 3\)[/tex]:
- If the translation rule is [tex]\((x, y) \rightarrow (x - 8, y + 3)\)[/tex], it implies that every point [tex]\( (x, y) \)[/tex] is translated to [tex]\( (x - 8) \)[/tex] in the x-direction and [tex]\( (y + 3) \)[/tex] in the y-direction.

After considering these options and evaluating which translation would be reasonable to complete the rule for all points, it appears that the most consistent y-translation that fits in this context is option 1.

Therefore, the translation rule for [tex]\(J\)[/tex] is:

[tex]\[ (x, y) \rightarrow (x - 8, y - 6) \][/tex]

So the answer is:
[tex]\[ y - 6 \][/tex]
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