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The rule as a mapping for the translation of a rectangle is [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex]. Which describes this translation?

A. A translation of 2 units down and 7 units to the right
B. A translation of 2 units down and 7 units to the left
C. A translation of 2 units to the right and 7 units up
D. A translation of 2 units to the left and 7 units up

Sagot :

GinnyAnswer
To determine which description accurately represents the given translation rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex], we need to analyze how the coordinates of any point [tex]\((x, y)\)[/tex] change according to this rule.

1. The new [tex]\(x\)[/tex]-coordinate is obtained by subtracting 2 from the original [tex]\(x\)[/tex]-coordinate: [tex]\(x-2\)[/tex]. This tells us that each point moves 2 units to the left along the [tex]\(x\)[/tex]-axis.

2. The new [tex]\(y\)[/tex]-coordinate is obtained by adding 7 to the original [tex]\(y\)[/tex]-coordinate: [tex]\(y+7\)[/tex]. This tells us that each point moves 7 units up along the [tex]\(y\)[/tex]-axis.

Putting these two observations together, the description that fits this translation rule is:

- A translation of 2 units to the left and 7 units up.

So the correct answer is:

a translation of 2 units to the left and 7 units up.
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