Alright, let's determine the rule for the given translation:
The problem states that a triangle is translated 4 units to the right and 3 units down. In coordinate geometry, translating a point involves shifting its [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-coordinates accordingly.
To translate a point [tex]\( (x, y) \)[/tex] 4 units to the right:
- We add 4 to the [tex]\( x \)[/tex]-coordinate. Therefore, the new [tex]\( x \)[/tex]-coordinate becomes [tex]\( x + 4 \)[/tex].
To translate a point [tex]\( (x, y) \)[/tex] 3 units down:
- We subtract 3 from the [tex]\( y \)[/tex]-coordinate. Therefore, the new [tex]\( y \)[/tex]-coordinate becomes [tex]\( y - 3 \)[/tex].
Putting it together, the rule for translating a point [tex]\( (x, y) \)[/tex] by 4 units right and 3 units down is:
[tex]\[ (x, y) \rightarrow (x + 4, y - 3) \][/tex]
Now let's compare this with the given options:
1. [tex]\( (x, y) \rightarrow (x + 3, y - 4) \)[/tex]
2. [tex]\( (x, y) \rightarrow (x + 3, y + 4) \)[/tex]
3. [tex]\( (x, y) \rightarrow (x + 4, y - 3) \)[/tex]
4. [tex]\( (x, y) \rightarrow (x + 4, y + 3) \)[/tex]
The correct rule that describes this translation is:
[tex]\[ (x, y) \rightarrow (x + 4, y - 3) \][/tex]
Thus, the correct answer is:
Option 3: [tex]\( (x, y) \rightarrow (x + 4, y - 3) \)[/tex]
