Determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E'?
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    A reflection of polygon ABCD across x-axis followed by a translation of 4 units to the left.

   Coordinates of a point A of polygon ABCD is (1, -5).

To map the polygon ABCD onto A'B'C'D',

Reflect the polygon ABCD across x-axis following the rule,

A(x, y) → A'(x, -y)

By this rule coordinates of A will be,

A(1, -5) → A'(1, 5)

Further ABCD is shifted by 4 units to the left,

Rule for the translation will be,

A'(x, y) → A"(x - 4, y)

A'(1, 5) → A"(1 - 4, 5)

           → A"(-3, 5)

     Therefore, polygon ABCD will overlap polygon A'B'C'D' by the series of transformations as,

A reflection of polygon ABCD across x-axis followed by a translation of 4 units to the left.

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Step-by-step explanation:

The transformations are:

You can deduct this transformations by using one vertex. Notice that E(4, -9) and E'(0, 9). You can observe that the transformed coordinate has the inverse y-coordinate, which indicates a x axis reflection. Also, it was shifted 4 units leftwards only.

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step-by-step explanation: