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Triangle ABC is translated according to the rule [tex]\((x, y) \rightarrow (x+2, y-8)\)[/tex]. If the coordinates of the pre-image of point [tex]\(B\)[/tex] are [tex]\((4, -5)\)[/tex], what are the coordinates of [tex]\(B'\)[/tex]?

A. [tex]\((2, 3)\)[/tex]
B. [tex]\((1, -9)\)[/tex]
C. [tex]\((-3, -4)\)[/tex]
D. [tex]\((6, -13)\)[/tex]

Sagot :

GinnyAnswer
To determine the coordinates of the point [tex]\( B' \)[/tex] after the translation, we will apply the given translation rule to the coordinates of the pre-image point [tex]\( B \)[/tex].

1. Identify the coordinates of the pre-image point [tex]\( B \)[/tex]:
- The pre-image coordinates of [tex]\( B \)[/tex] are [tex]\( (4, -5) \)[/tex].

2. Understand the translation rule:
- The translation rule provided is [tex]\( (x, y) \rightarrow (x + 2, y - 8) \)[/tex]. This means that to find the coordinates of the image after translation, we need to:
- Add 2 to the x-coordinate.
- Subtract 8 from the y-coordinate.

3. Apply the translation to the x-coordinate:
- The original x-coordinate is 4.
- Adding 2 to the x-coordinate: [tex]\( 4 + 2 = 6 \)[/tex].

4. Apply the translation to the y-coordinate:
- The original y-coordinate is -5.
- Subtracting 8 from the y-coordinate: [tex]\( -5 - 8 = -13 \)[/tex].

5. Determine the new coordinates:
- After the translation, the new coordinates [tex]\( (x', y') \)[/tex] of [tex]\( B' \)[/tex] are [tex]\( (6, -13) \)[/tex].

Therefore, the coordinates of [tex]\( B' \)[/tex] are [tex]\( (6, -13) \)[/tex].

The correct answer is:
[tex]\[ (6, -13) \][/tex]
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