Question

determine a series of transformations that would map polygon abcd onto polygon abcd. a followed by a

Explanation:

Step1: Observe orientation change

Notice that the orientation of polygon \(ABCD\) is flipped to get polygon \(A'B'C'D'\). A reflection over the \(x\) - axis changes the sign of the \(y\) - coordinates of all points. Let \((x,y)\) be a point on polygon \(ABCD\), after reflection over the \(x\) - axis, it becomes \((x, - y)\).

Step2: Observe vertical and horizontal shift

After reflection, we need to shift the polygon. Counting the units, we find that after reflection, we need to shift the polygon 1 unit to the right and 4 units up. If a point \((x,y)\) is reflected over the \(x\) - axis to get \((x,-y)\), then after translation \(1\) unit right and \(4\) units up, it becomes \((x + 1,-y+4)\).

Answer:

A reflection over the \(x\) - axis followed by a translation 1 unit to the right and 4 units up.