To determine the correct function rule for translating a square on a coordinate plane, we need to consider the effect of the translation on the coordinates of any point [tex]\((x, y)\)[/tex] on the square.
When a figure is translated:
- Horizontally by [tex]\( h \)[/tex] units, each [tex]\( x \)[/tex]-coordinate of the points on the figure is adjusted by adding [tex]\( h \)[/tex].
- Vertically by [tex]\( k \)[/tex] units, each [tex]\( y \)[/tex]-coordinate of the points on the figure is adjusted by adding [tex]\( k \)[/tex].
The general translation function rule can be expressed as [tex]\( T_{h, k}(x, y) \)[/tex], where:
- [tex]\( h \)[/tex] represents the horizontal translation.
- [tex]\( k \)[/tex] represents the vertical translation.
For this specific problem:
1. The square is translated 1 unit to the right.
- Moving to the right corresponds to a positive horizontal translation. Hence, [tex]\( h = 1 \)[/tex].
2. The square is translated 9 units down.
- Moving downward corresponds to a negative vertical translation. Hence, [tex]\( k = -9 \)[/tex].
Therefore, the function rule that describes this translation is [tex]\( T_{1, -9}(x, y) \)[/tex].
To summarize, the correct function rule is:
[tex]\[ T_{1, -9}(x, y) \][/tex]
