A triangle on a coordinate plane is translated according to the rule [tex]$T_{-3,5}(x, y)$[/tex]. Which is another way to write this rule?

A. [tex]$(x, y) \rightarrow (x-3, y+5)$[/tex]
B. [tex][tex]$(x, y) \rightarrow (x-3, y-5)$[/tex][/tex]
C. [tex]$(x, y) \rightarrow (x+3, y-5)$[/tex]
D. [tex]$(x, y) \rightarrow (x+3, y+5)$[/tex]



Answer :

To understand how to rewrite the translation rule [tex]\( T_{-3,5}(x, y) \)[/tex], let’s break down the components of what this translation means.

The given translation rule is [tex]\( T_{-3,5}(x, y) \)[/tex]. This notation indicates that every point [tex]\((x, y)\)[/tex] on the coordinate plane is being translated as follows:
- The x-coordinate of the point is shifted by [tex]\(-3\)[/tex].
- The y-coordinate of the point is shifted by [tex]\(+5\)[/tex].

Let’s translate a generic point [tex]\((x, y)\)[/tex] with this rule:
- The new x-coordinate will be [tex]\( x - 3 \)[/tex]:
[tex]\[ \text{New x-coordinate} = x - 3 \][/tex]
- The new y-coordinate will be [tex]\( y + 5 \)[/tex]:
[tex]\[ \text{New y-coordinate} = y + 5 \][/tex]

Combining these, we find that the translation rule transforms the point [tex]\((x, y)\)[/tex] to:
[tex]\[ (x, y) \rightarrow (x-3, y+5) \][/tex]

Now we shall review the given options to see which matches this resultant transformation:
1. [tex]\((x, y) \rightarrow(x-3, y+5)\)[/tex]
2. [tex]\((x, y) \rightarrow(x-3, y-5)\)[/tex]
3. [tex]\((x, y) \rightarrow(x+3, y-5)\)[/tex]
4. [tex]\((x, y) \rightarrow(x+3, y+5)\)[/tex]

From our transformation [tex]\( (x, y) \rightarrow(x-3, y+5) \)[/tex], the correct option is:
[tex]\[ (x, y) \rightarrow (x-3, y+5) \][/tex]

Therefore, the correct option is the first one:
[tex]\[ \boxed{(x, y) \rightarrow (x-3, y+5)} \][/tex]