Question

determine a series of transformations that would map polygon ( abcde ) onto polygon ( abcde ).

Explanation:

Step1: Analyze the reflection

The original polygon \(ABCDE\) and the image \(A'B'C'D'E'\) are mirror - images with respect to the \(y\) - axis. The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Analyze the translation

After reflection over the \(y\) - axis, we need to translate the reflected polygon. Let's take a point, say \(A(1, - 2)\). After reflection over the \(y\) - axis, it becomes \((-1,-2)\). The image point \(A'(-11,-2)\). The \(x\) - coordinate changes from \(-1\) to \(-11\) (a change of \(-10\) in the \(x\) - direction). The translation rule is \((x,y)\to(x - 10,y)\)

Answer:

A reflection over the \(y\) - axis followed by a translation \(10\) units to the left.