The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). Which describes this translation?

Question

a translation of 2 units down and 7 units to the right
a translation of 2 units down and 7 units to the left
a translation of 2 units to the right and 7 units up
a translation of 2 units to the left and 7 units up

Answer 1

The given mapping for the translation of a rectangle is expressed as \((x, y) \rightarrow (x - 2, y + 7)\).

To analyze the translation:

• The \(x\) coordinate changes from \(x\) to \(x - 2\), which means it moves 2 units to the left (since we are subtracting 2).
• The \(y\) coordinate changes from \(y\) to \(y + 7\), which means it moves 7 units up (since we are adding 7).

Thus, the translation described is:

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