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A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

A. [tex]\((x, y) \rightarrow (x+5, y-3)\)[/tex]
B. [tex]\((x, y) \rightarrow (x+5, y+3)\)[/tex]
C. [tex]\((x, y) \rightarrow (x-3, y+5)\)[/tex]
D. [tex]\((x, y) \rightarrow (x+3, y+5)\)[/tex]

Sagot :

GinnyAnsweridn
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]
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