Question

a figure is translated using the rule $(x,y)\to(x - 3,y + 6)$.which describes how the figure is moved?left 3 units and down 6 unitsleft 3 units and up 6 unitsright 3 units and down 6 unitsleft 6 units and down 3 units

Explanation:

Step1: Analyze the x - coordinate transformation

In the translation rule \((x,y)\to(x - 3,y+6)\), for the \(x\) - coordinate, we have \(x\to x - 3\). According to the translation property (if \(x\to x - a\) where \(a>0\), the figure moves \(a\) units to the left). Here \(a = 3\), so the figure moves 3 units to the left.

Step2: Analyze the y - coordinate transformation

For the \(y\) - coordinate, we have \(y\to y + 6\). According to the translation property (if \(y\to y + b\) where \(b>0\), the figure moves \(b\) units up). Here \(b = 6\), so the figure moves 6 units up.

Answer:

left 3 units and up 6 units