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]
