Question

question determine a series of transformations that would map polygon abcde onto polygon abcde. a reflection over the y - axis followed by a dilation centered at the origin with a scale factor of.

Explanation:

Step1: Observe orientation change

The orientation of polygon \(ABCDE\) is reversed in \(A'B'C'D'E'\), which can be achieved by a reflection over the y - axis. The rule for a reflection over the y - axis is \((x,y)\to(-x,y)\).

Step2: Observe size change

The polygon \(A'B'C'D'E'\) is larger than \(ABCDE\). To change the size, a dilation is needed. Count the distance between corresponding points. For example, if we consider a point \(A(3,1)\) and its corresponding point \(A'(- 9,3)\). The ratio of the x - coordinates \(\frac{-9}{-3}=3\) and the ratio of the y - coordinates \(\frac{3}{1} = 3\). So the scale factor of the dilation centered at the origin \((0,0)\) is \(3\). The rule for a dilation centered at the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\).

Answer:

A reflection over the y - axis followed by a dilation centered at the origin with a scale factor of \(3\).