Question

a figure is translated using the rule (x, y) → (x − 3, y + 6). which describes how the figure is moved? ○ left 3 units and down 6 units ○ right 3 units and down 6 units ○ left 6 units and down 3 units ○ left 3 units and up 6 units

Explanation:

Step1: Analyze x - coordinate change

In the translation rule \((x,y)\to(x - 3,y + 6)\), for the x - coordinate, we have \(x\) changing to \(x-3\). In the coordinate system, a decrease in the x - value (subtracting a positive number from \(x\)) means a shift to the left. So, the figure moves 3 units to the left in the x - direction.

Step2: Analyze y - coordinate change

For the y - coordinate, we have \(y\) changing to \(y + 6\). In the coordinate system, an increase in the y - value (adding a positive number to \(y\)) means a shift up. So, the figure moves 6 units up in the y - direction.

Answer:

left 3 units and up 6 units (the last option: left 3 units and up 6 units)