To determine the rule that describes the translation of a rectangle on a coordinate plane, we need to understand the effect of translating a point by a given number of units up or down and left or right.
Here is the step-by-step process:
1. Translation Up:
- Translating a point 5 units up means increasing the y-coordinate by 5. If a point is [tex]\((x, y)\)[/tex], after translating it 5 units up, the new position will be [tex]\((x, y + 5)\)[/tex].
2. Translation to the Left:
- Translating a point 3 units to the left means decreasing the x-coordinate by 3. If a point is [tex]\((x, y)\)[/tex], after translating it 3 units to the left, the new position will be [tex]\((x - 3, y)\)[/tex].
Combining these two effects, if we start with a point [tex]\((x, y)\)[/tex]:
- After moving 5 units up: The point becomes [tex]\((x, y + 5)\)[/tex].
- After then moving 3 units to the left: The point becomes [tex]\((x - 3, y + 5)\)[/tex].
Therefore, 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]
Thus, the correct answer is:
[tex]\((x, y) \rightarrow (x - 3, y + 5)\)[/tex].
