To understand how to describe the translation of a triangle on the coordinate plane, we need to examine how translations affect the coordinates of the points that make up the triangle.
### Translation Right by 4 Units:
- When a point [tex]\((x, y)\)[/tex] is translated 4 units to the right, we add 4 to its x-coordinate.
- Hence, the new x-coordinate will be [tex]\(x + 4\)[/tex].
### Translation Down by 3 Units:
- When a point [tex]\((x, y)\)[/tex] is translated 3 units down, we subtract 3 from its y-coordinate.
- Hence, the new y-coordinate will be [tex]\(y - 3\)[/tex].
We combine these translations to get the new coordinates:
- The original point [tex]\((x, y)\)[/tex] will be transformed to [tex]\((x + 4, y - 3)\)[/tex] after translating 4 units to the right and 3 units down.
So the rule describing the translation is:
[tex]\[
(x, y) \rightarrow (x + 4, y - 3)
\][/tex]
Among the given options, the correct rule is:
[tex]\[
(x, y) \rightarrow (x+4, y-3)
\][/tex]
Therefore, the correct rule that describes the translation is [tex]\((x, y) \rightarrow (x+4, y-3)\)[/tex].
