Question

a translation left 6 units and down 6 units.

Explanation:

Step1: Analyze the horizontal movement

To find the horizontal translation, compare the \(x -\)coordinates of corresponding points of Figure \(R\) and Figure \(S\). Let's take a vertex of Figure \(R\) (say \((- 2,6)\)) and the corresponding vertex of Figure \(S\) (say \((-8,0)\)). The change in the \(x -\)coordinate is \(\Delta x=x_{S}-x_{R}\). If \(x_{R}=-2\) and \(x_{S}=-8\), then \(\Delta x=-8 - (-2)=-6\). A negative change in the \(x -\)coordinate means a translation to the left.

Step2: Analyze the vertical movement

To find the vertical translation, compare the \(y -\)coordinates of corresponding points. Using the same pair of points \((-2,6)\) (from Figure \(R\)) and \((-8,0)\) (from Figure \(S\)), the change in the \(y -\)coordinate is \(\Delta y=y_{S}-y_{R}\). If \(y_{R} = 6\) and \(y_{S}=0\), then \(\Delta y=0 - 6=-6\). A negative change in the \(y -\)coordinate means a translation downwards.

Answer:

A translation left \(6\) units and down \(6\) units.