To determine which rule describes the translation of a rectangle on a coordinate plane when it is translated 5 units up and 3 units to the left, let's analyze what happens to the coordinates of any point [tex]\((x, y)\)[/tex] during this translation.
1. Translation 5 units up:
- When you move a point 5 units up, you are increasing the y-coordinate by 5. So, the new y-coordinate will be [tex]\(y + 5\)[/tex].
2. Translation 3 units to the left:
- When you move a point 3 units to the left, you are decreasing the x-coordinate by 3. So, the new x-coordinate will be [tex]\(x - 3\)[/tex].
Combining these two transformations, the rule for the translation can be described as:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
Therefore, the rule that describes the translation is:
[tex]\[ (x, y) \rightarrow (x-3, y+5) \][/tex]
