To determine the rule that describes the translation of a rectangle on a coordinate plane, let's break down the translation step-by-step.
1. Translation 5 Units Up:
- When a point is translated 5 units up, its [tex]\( y \)[/tex]-coordinate increases by 5. Therefore, if the original coordinates of the point are [tex]\((x, y)\)[/tex], the new [tex]\( y \)[/tex]-coordinate after translating up 5 units will be [tex]\( y + 5 \)[/tex].
2. Translation 3 Units to the Left:
- When a point is translated 3 units to the left, its [tex]\(x\)[/tex]-coordinate decreases by 3. Therefore, if the original coordinates of the point are [tex]\((x, y)\)[/tex], the new [tex]\(x\)[/tex]-coordinate after translating left 3 units will be [tex]\( x - 3 \)[/tex].
Combining these two transformations, the point originally at [tex]\((x, y)\)[/tex] will be moved to [tex]\((x - 3, y + 5)\)[/tex].
Thus, the rule describing this translation is:
[tex]\[
(x, y) \rightarrow (x - 3, y + 5)
\][/tex]
Therefore, the correct rule is:
[tex]\[
(x, y) \rightarrow (x - 3, y + 5)
\][/tex]
