Question

determine a series of transformations that would map figure p onto figure q.
answer
a reflection over the x - axis followed by a translation left 7 unit(s).

Explanation:

Step1: Analyze the orientation of the figures

Figure \(P\) is below the \(x -\)axis and Figure \(Q\) is above the \(x -\)axis. A reflection over the \(x -\)axis changes the sign of the \(y -\)coordinate of each point. If we have a point \((x,y)\) on Figure \(P\), after reflection over the \(x -\)axis, it becomes \((x, - y)\).

Step2: Analyze the horizontal translation

After reflection over the \(x -\)axis, we need to move the reflected figure to the left. Counting the horizontal distance between the corresponding points of the reflected - over - \(x -\)axis Figure \(P\) and Figure \(Q\). We can see that we need to move the figure \(7\) units to the left. A translation to the left \(h\) units changes the \(x -\)coordinate of each point \((x,y)\) to \((x - h,y)\)

Answer:

A reflection over the \(x -\)axis followed by a translation left \(7\) unit(s).