To determine the correct rule that describes the given translation of a rectangle on a coordinate plane, we need to carefully understand the effects of the translation described.
### Translation Details:
1. Translation 5 units up: This means that we are moving every point of the rectangle 5 units vertically upwards. Mathematically, this operation increases the y-coordinate by 5.
2. Translation 3 units to the left: This means that we are moving every point of the rectangle 3 units horizontally to the left. Mathematically, this operation decreases the x-coordinate by 3.
### Combining Both Translations:
- For any point [tex]\((x, y)\)[/tex] on the rectangle:
- The y-coordinate will be adjusted by adding 5 to it (since we are moving up).
- The x-coordinate will be adjusted by subtracting 3 from it (since we are moving to the left).
So, the new coordinates [tex]\((x', y')\)[/tex] of the point after applying the translation will be:
[tex]\[
(x', y') = (x-3, y+5)
\][/tex]
### Translation Rule:
Thus, the rule describing this translation on the coordinate plane is:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
### Answer Choices Analysis:
- [tex]\((x, y) \rightarrow (x+5, y-3)\)[/tex] moves right 5 units and down 3 units (incorrect).
- [tex]\((x, y) \rightarrow (x+5, y+3)\)[/tex] moves right 5 units and up 3 units (incorrect).
- [tex]\((x, y) \rightarrow (x-3, y+5)\)[/tex] moves left 3 units and up 5 units (correct).
- [tex]\((x, y) \rightarrow (x+3, y+5)\)[/tex] moves right 3 units and up 5 units (incorrect).
Therefore, the rule describing the translation of a rectangle 5 units up and 3 units to the left is:
\[
(x,y) \rightarrow (x-3, y+5)
\
