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Points [tex]$R, S$[/tex], and [tex]$T$[/tex] have the coordinates [tex]$R(-5,8), S(-6,14)$[/tex], and [tex]$T(-9,-6)$[/tex]. Together the points make a triangle. If the triangle was translated so that point [tex]$R$[/tex] ended up at the coordinates [tex]$(5,4)$[/tex], what would be the new coordinates of point [tex]$S$[/tex]?

A. [tex]$(-3,13)$[/tex]
B. [tex]$(-1,3)$[/tex]
C. [tex]$(4,10)$[/tex]
D. [tex]$(7,5)$[/tex]



Answer :

GinnyAnswer
To determine the new coordinates of point [tex]\( S \)[/tex] after translating the triangle so that point [tex]\( R \)[/tex] moves from [tex]\((-5, 8)\)[/tex] to [tex]\((5, 4)\)[/tex], follow these steps:

1. Calculate the translation vector:
- Point [tex]\( R \)[/tex] moves from [tex]\((-5, 8)\)[/tex] to [tex]\((5, 4)\)[/tex].
- The translation vector is the difference between these coordinates:
[tex]\[ (5 - (-5), 4 - 8) = (10, -4) \][/tex]

2. Apply the translation vector to point [tex]\( S \)[/tex]:
- Point [tex]\( S \)[/tex] originally has coordinates [tex]\((-6, 14)\)[/tex].
- Add the translation vector [tex]\((10, -4)\)[/tex] to these coordinates:
[tex]\[ (-6 + 10, 14 - 4) = (4, 10) \][/tex]

Thus, the new coordinates of point [tex]\( S \)[/tex] after the translation are:
[tex]\[ \boxed{(4, 10)} \][/tex]

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