Question

question
determine a series of transformations that would map polygon ( a b c d e ) onto polygon ( a ^ { prime } b ^ { prime } c ^ { prime } d ^ { prime } e ^ { prime } ).

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 flip the polygon \(ABCDE\) vertically.

Step2: Translate

After reflection, we need to translate the polygon. Let's assume a translation of \((x,y)\to(x + h,y + k)\). By comparing the coordinates of corresponding vertices (for example, if \(A=(0, - 1)\) after reflection and \(A'=(1,-9)\), we find that \(h = 1-0=1\) and \(k=-9-(1)= - 8\)). The translation rule is \((x,y)\to(x + 1,y-8)\)

Answer:

Reflect polygon \(ABCDE\) over the \(x\) - axis and then translate it \(1\) unit to the right and \(8\) units down.