Question

a figure is translated using the mapping $(x, y) \to (x + a, y + b)$. if the value of $a$ is negative and the value of $b$ is negative, which best describes the translation? \bigcirc the figure moves left and up. \bigcirc the figure moves left and down. \bigcirc the figure moves right and up. \bigcirc the figure moves right and down.

Explanation:

In a translation mapping \((x, y) \to (x + a, y + b)\), for the \(x\)-coordinate: a positive \(a\) moves right, a negative \(a\) moves left. For the \(y\)-coordinate: a positive \(b\) moves up, a negative \(b\) moves down. Since \(a\) and \(b\) are negative, the figure moves left (from \(x + a\) with negative \(a\)) and down (from \(y + b\) with negative \(b\)).

Answer:

The figure moves left and down.