Use the graph to answer the question.

Question

graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at negative 7 comma 5, negative 5 comma 1, negative 1 comma 1, negative 3 comma 5

Determine the translation used to create the image.
4 units to the right
4 units to the left
8 units to the right
8 units to the left

Answer 1

To determine the translation used to create the image polygon \( A'B'C'D' \) from the original polygon \( ABCD \), we need to compare the coordinates of the corresponding vertices in both polygons.

Original Polygon ABCD:

• \( A(1, 5) \)
• \( B(3, 1) \)
• \( C(7, 1) \)
• \( D(5, 5) \)

Transformed Polygon A'B'C'D':

• \( A'(-7, 5) \)
• \( B'(-5, 1) \)
• \( C'(-1, 1) \)
• \( D'(-3, 5) \)

Analyzing the Translation:

1. For Vertex A:

   • \( A(1, 5) \) to \( A'(-7, 5) \)
   • The x-coordinate changes from \( 1 \) to \( -7 \), which is a change of \( -8 \) units (1 - (-7) = -8).

2. For Vertex B:

   • \( B(3, 1) \) to \( B'(-5, 1) \)
   • The x-coordinate changes from \( 3 \) to \( -5 \), which is also a change of \( -8 \) units (3 - (-5) = -8).

3. For Vertex C:

   • \( C(7, 1) \) to \( C'(-1, 1) \)
   • The x-coordinate changes from \( 7 \) to \( -1 \), which is again a change of \( -8 \) units (7 - (-1) = -8).

4. For Vertex D:

   • \( D(5, 5) \) to \( D'(-3, 5) \)
   • The x-coordinate changes from \( 5 \) to \( -3 \), which is once more a change of \( -8 \) units (5 - (-3) = -8).

Conclusion:

All vertices confirm a consistent translation of \( 8 \) units to the left.

Thus, the translation used to create the image is 8 units to the left.