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Use the graph to answer the question.

Graph of polygon ABCD with vertices at 0 comma 5, 2 comma 1, 6 comma 1, 4 comma 5. A second polygon A prime B prime C prime D prime with vertices at 0 comma negative 2, 2 comma negative 6, 6 comma negative 6, 4 comma negative 2.

Determine the translation used to create the image.
3 units down
3 units up
7 units down
7 units up

1 answer

To determine the translation used to create the image from polygon ABCD to polygon A'B'C'D', we compare the y-coordinates of corresponding vertices of the two polygons.

  1. Vertex A (0, 5) translates to A' (0, -2):

    • The change in y-coordinate is: \(-2 - 5 = -7\)

  2. Vertex B (2, 1) translates to B' (2, -6):

    • The change in y-coordinate is: \(-6 - 1 = -7\)

  3. Vertex C (6, 1) translates to C' (6, -6):

    • The change in y-coordinate is: \(-6 - 1 = -7\)

  4. Vertex D (4, 5) translates to D' (4, -2):

    • The change in y-coordinate is: \(-2 - 5 = -7\)

All corresponding vertices of the two polygons have a consistent change in the y-coordinates of -7. This means that the translation is 7 units down.

Therefore, the correct answer is: 7 units down.