To solve the problem of determining the correct translation function rule for moving a square 9 units down and 1 unit to the right, let's start by understanding how translations work on a coordinate plane.
A translation moves every point of a figure the same distance in the same direction. The general form for a translation is:
[tex]\[ T_{a,b}(x, y) \][/tex]
where [tex]\( T_{a,b} \)[/tex] denotes a translation function that moves a point [tex]\((x, y)\)[/tex].
- [tex]\(a\)[/tex] represents the horizontal change: positive for right and negative for left.
- [tex]\(b\)[/tex] represents the vertical change: positive for up and negative for down.
In this case:
- Moving 1 unit to the right is a horizontal shift of [tex]\( +1 \)[/tex].
- Moving 9 units down is a vertical shift of [tex]\( -9 \)[/tex].
Thus, combining these shifts, the correct translation function [tex]\( T_{a,b}(x, y) \)[/tex] would be:
[tex]\[ T_{1, -9}(x, y) \][/tex]
This notation means:
[tex]\[ (x, y) \rightarrow (x + 1, y - 9) \][/tex]
Given the choices:
a) [tex]\( T_{1, -9}(x, y) \)[/tex]
b) [tex]\( T_{-1,-G}(x, y) \)[/tex]
c) [tex]\( T_{-9,1}(x, y) \)[/tex]
d) [tex]\( T_{-,-1}(x, y) \)[/tex]
Choice (a) [tex]\( T_{1, -9}(x, y) \)[/tex] correctly represents the translation of 1 unit to the right and 9 units down.
Therefore, the function rule that describes this translation is:
[tex]\[ \boxed{a \; T_{1, -9}(x, y)} \][/tex]
