To determine the rule used to translate the triangle, let's first focus on the coordinates of point [tex]\( L \)[/tex]. The original coordinates of point [tex]\( L \)[/tex] are [tex]\( (7, -3) \)[/tex], and the new coordinates after translation, [tex]\( L' \)[/tex], are [tex]\( (-1, 8) \)[/tex].
To find the translation rule, we need to determine how much the [tex]\( x \)[/tex]-coordinate and the [tex]\( y \)[/tex]-coordinate have changed.
1. Calculate the change in the [tex]\( x \)[/tex]-coordinate:
[tex]\[
\Delta x = x' - x = -1 - 7 = -8
\][/tex]
2. Calculate the change in the [tex]\( y \)[/tex]-coordinate:
[tex]\[
\Delta y = y' - y = 8 - (-3) = 8 + 3 = 11
\][/tex]
So, the translation changes each point [tex]\((x, y)\)[/tex] by [tex]\((x - 8)\)[/tex] and [tex]\((y + 11)\)[/tex].
Hence, the translation rule is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
The correct translation rule is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
Therefore, the correct option is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
