To determine how the rule [tex]\( T_{-3,5}(x, y) \)[/tex] translates a point on the coordinate plane, let's break down the components of the translation rule [tex]\( T_{-3,5} \)[/tex].
The notation [tex]\( T_{-3,5}(x, y) \)[/tex] signifies that each point [tex]\((x, y)\)[/tex] on the plane is being translated:
- The [tex]\( -3 \)[/tex] indicates a translation 3 units to the left along the x-axis.
- The [tex]\( 5 \)[/tex] indicates a translation 5 units up along the y-axis.
By applying these translations, we can express the new coordinates of a point [tex]\((x, y)\)[/tex] as follows:
1. Adjust the x-coordinate: Move the x-coordinate [tex]\( x \)[/tex] left by 3 units. Mathematically, this is represented by [tex]\( x - 3 \)[/tex].
2. Adjust the y-coordinate: Move the y-coordinate [tex]\( y \)[/tex] up by 5 units. Mathematically, this is represented by [tex]\( y + 5 \)[/tex].
Thus, the translation [tex]\( T_{-3,5}(x, y) \)[/tex] can be rewritten as:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
This transformation rule indicates that each point [tex]\((x, y)\)[/tex] is mapped to a new point [tex]\((x - 3, y + 5)\)[/tex]. Therefore, the correct way to write this rule is:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
So, out of the given options:
- [tex]\((x, y) \rightarrow (x - 3, y + 5)\)[/tex]
- [tex]\((x, y) \rightarrow (x - 3, y - 5)\)[/tex]
- [tex]\((x, y) \rightarrow (x + 3, y - 5)\)[/tex]
- [tex]\((x, y) \rightarrow (x + 3, y + 5)\)[/tex]
The correct translation corresponding to the rule [tex]\( T_{-3,5}(x, y) \)[/tex] is:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
