To determine the rule that describes the translation of a rectangle on a coordinate plane by 5 units up and 3 units to the left, let's analyze the translation in steps:
1. Translation of 3 units to the left:
- Moving to the left affects the x-coordinate.
- When moving left, the x-coordinate decreases.
- Therefore, the x-coordinate will be reduced by 3 units.
- If the original coordinate is [tex]\((x, y)\)[/tex], after moving left the new coordinate will be [tex]\((x-3, y)\)[/tex].
2. Translation of 5 units up:
- Moving up affects the y-coordinate.
- When moving up, the y-coordinate increases.
- Therefore, the y-coordinate will be increased by 5 units.
- For the coordinate [tex]\((x-3, y)\)[/tex] (after moving left), moving up will result in the new coordinate becoming [tex]\((x-3, y+5)\)[/tex].
Combining the effects of both translations, the rule that describes this translation is:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
Thus, the rule that describes the translation of the rectangle 5 units up and 3 units to the left is:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
Therefore, the correct answer is:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
