Question

which of the following transformations represents a translation 3 units right and 2 units down?
$(x, y) \mapsto (x - 3, y + 2)$
$(x, y) \mapsto (x - 3, y - 2)$
$(x, y) \mapsto (x + 3, y + 2)$
$(x, y) \mapsto (x + 3, y - 2)$

Explanation:

Step1: Recall translation rules

For a translation, moving right/left affects the \(x\)-coordinate (right: \(+x\), left: \(-x\)) and moving up/down affects the \(y\)-coordinate (up: \(+y\), down: \(-y\)).

Step2: Analyze 3 units right

Moving 3 units right means we add 3 to the \(x\)-coordinate, so \(x\) becomes \(x + 3\).

Step3: Analyze 2 units down

Moving 2 units down means we subtract 2 from the \(y\)-coordinate, so \(y\) becomes \(y - 2\).

Step4: Determine the transformation

Combining these, the transformation should be \((x, y) \to (x + 3, y - 2)\).

Answer:

\((x, y) \to (x + 3, y - 2)\) (the fourth option)