Use the graph to answer the question.

Question

Graph of polygon ABCD with vertices at negative 2 comma negative 1, 0 comma negative 4, 4 comma negative 4, 2 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 5 comma negative 1, 7 comma negative 4, 11 comma negative 4, 9 comma negative 1.

Determine the translation used to create the image.
7 units to the right
3 units to the right
7 units to the left
3 units to the left

Answer 1

To determine the translation used to create the image of polygon ABCD into polygon A'B'C'D', we can analyze the coordinates of the corresponding vertices of the two polygons.

For polygon ABCD:

• A (-2, -1)
• B (0, -4)
• C (4, -4)
• D (2, -1)

For polygon A'B'C'D':

• A' (5, -1)
• B' (7, -4)
• C' (11, -4)
• D' (9, -1)

Now, let's find the translation for the x-coordinates of one pair of corresponding vertices (we can check just one pair, as the same translation should apply to all pairs):

1. From A (-2, -1) to A' (5, -1):

   • The x-coordinate goes from -2 to 5.
   • The change in x is \( 5 - (-2) = 5 + 2 = 7 \).

2. Now, let's confirm this with another pair, say B (0, -4) to B' (7, -4):

   • The x-coordinate goes from 0 to 7.
   • The change in x is \( 7 - 0 = 7 \).

This confirms the translation. All corresponding x-coordinates are increasing by 7 units.

Thus, the translation used to create the image is 7 units to the right.