Use the graph to answer the question.

Question

Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at negative 6 comma negative 1, negative 4 comma negative 5, 0 comma negative 5, negative 2 comma negative 1.

Determine the translation used to create the image.
5 units to the right
1 unit to the right
5 units to the left
1 unit to the left

Answer 1

To determine the translation used to create the image of polygon ABCD to A'B'C'D', we need to compare the coordinates of the vertices of both polygons.

1. Vertices of polygon ABCD:

   • A: (-1, -1)
   • B: (1, -5)
   • C: (5, -5)
   • D: (3, -1)

2. Vertices of polygon A'B'C'D':

   • A': (-6, -1)
   • B': (-4, -5)
   • C': (0, -5)
   • D': (-2, -1)

Next, we analyze the changes in the x-coordinates of the corresponding vertices:

• For vertex A to A':

  • From -1 to -6: shifted left by 5 units.

• For vertex B to B':

  • From 1 to -4: shifted left by 5 units.

• For vertex C to C':

  • From 5 to 0: shifted left by 5 units.

• For vertex D to D':

  • From 3 to -2: shifted left by 5 units.

We see that each vertex has been translated consistently to the left by 5 units.

Therefore, the translation used to create the image is 5 units to the left.