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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 B 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 solve this problem, we need to apply the given translation rule to the coordinates of point B. The rule we are given is [tex]\((x, y) \rightarrow (x + 2, y - 8)\)[/tex].

Step-by-step, here's how we proceed:

1. Start with the given coordinates of point B, which are [tex]\((4, -5)\)[/tex].

2. Apply the translation rule:
- For the x-coordinate: [tex]\(x + 2 = 4 + 2\)[/tex]
- For the y-coordinate: [tex]\(y - 8 = -5 - 8\)[/tex]

3. Perform the calculations:
- [tex]\(4 + 2 = 6\)[/tex]
- [tex]\(-5 - 8 = -13\)[/tex]

So, after applying the translation, the new coordinates of [tex]\(B^\prime\)[/tex] are [tex]\((6, -13)\)[/tex].

Therefore, the coordinates of [tex]\(B^\prime\)[/tex] are [tex]\((6, -13)\)[/tex], so the correct choice is:
[tex]\((6, -13)\)[/tex].
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