To find the translation rule that was used to move right triangle [tex]\( \Delta LMN \)[/tex] such that point [tex]\( L \)[/tex] with coordinates [tex]\( (7, -3) \)[/tex] moved to point [tex]\( L' \)[/tex] with coordinates [tex]\( (-1, 8) \)[/tex], follow these steps:
1. Initial and Final Coordinates:
- Initial coordinates of [tex]\( L \)[/tex]: [tex]\( (7, -3) \)[/tex]
- Final coordinates of [tex]\( L' \)[/tex]: [tex]\( (-1, 8) \)[/tex]
2. Calculate Translation Change:
- To find the change in the x-coordinate, subtract the initial x-coordinate from the final x-coordinate:
[tex]\[
x_{\text{change}} = x' - x = -1 - 7 = -8
\][/tex]
- To find the change in the y-coordinate, subtract the initial y-coordinate from the final y-coordinate:
[tex]\[
y_{\text{change}} = y' - y = 8 - (-3) = 8 + 3 = 11
\][/tex]
3. Translation Rule:
- The translation rule can be written as: [tex]\( (x, y) \rightarrow (x + x_{\text{change}}, y + y_{\text{change}}) \)[/tex]
- Based on our calculations:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
Therefore, the correct translation rule used is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
The correct option is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 11)
\][/tex]
