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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]\(B^{\prime}\)[/tex]?

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



Answer :

GinnyAnswer
Sure! To solve this problem, we'll take the given pre-image coordinates of point B and apply the translation rule step-by-step.

The initial coordinates of point B are given as (4, -5).

The translation rule provided is:
[tex]\[ (x, y) \rightarrow (x+2, y-8) \][/tex]

This means:
- We need to add 2 to the x-coordinate.
- We need to subtract 8 from the y-coordinate.

Let's apply the rule to the given point:

1. Start with the x-coordinate:
- Original x-coordinate: [tex]\(4\)[/tex]
- Apply the translation: [tex]\(4 + 2 = 6\)[/tex]

2. Now for the y-coordinate:
- Original y-coordinate: [tex]\(-5\)[/tex]
- Apply the translation: [tex]\(-5 - 8 = -13\)[/tex]

Therefore, after applying the translation rule, the new coordinates of point [tex]\(B'\)[/tex] are [tex]\((6, -13)\)[/tex].

So the coordinates of [tex]\(B'\)[/tex] are:
[tex]\[ \boxed{(6, -13)} \][/tex]

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