Question

determine a series of transformations that would map figure p onto figure q.

Explanation:

Step1: Reflect over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). This will change the sign of the \(y\) - coordinate of each vertex of Figure \(P\).

Step2: Translate 8 units left

The translation rule for moving a point \((x,y)\) \(8\) units to the left is \((x,y)\to(x - 8,y)\). After reflection over the \(x\) - axis, applying this translation will map the reflected figure onto Figure \(Q\).

Answer:

First, reflect Figure \(P\) over the \(x\) - axis. Then, translate the resulting figure \(8\) units to the left.