Use the graph to answer the question.

Question

Graph of polygon ABCDE with vertices at negative 1 comma negative 4, negative 1 comma negative 1, 3 comma negative 1, 3 comma negative 4, 1 comma negative 6. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma negative 4, 13 comma negative 1, 9 comma negative 1, 9 comma negative 4, 11 comma negative 6.

Determine the line of reflection.
Reflection across the x-axis
Reflection across x = 6
Reflection across y = −3
Reflection across the y-axis

Answer 1

To determine the line of reflection between the two polygons ABCDE and A'B'C'D'E', we can consider the transformation that takes points from one polygon to the other.

1. Finding the midpoint of corresponding points: Let's take the coordinates of a few corresponding points from both polygons. For example:

   • A(-1, -4) and A'(13, -4)
   • B(-1, -1) and B'(13, -1)
   • C(3, -1) and C'(9, -1)
   • D(3, -4) and D'(9, -4)
   • E(1, -6) and E'(11, -6)

   Each pair of points has the same y-coordinate, indicating that the reflection happens horizontally.

2. Finding the line of reflection: To find the line of reflection for each pair of points, consider the x-coordinates:

   • For A and A', the average x-coordinate is \((-1 + 13)/2 = 6\).
   • For B and B', the average x-coordinate is \((-1 + 13)/2 = 6\).
   • For C and C', the average x-coordinate is \((3 + 9)/2 = 6\).
   • For D and D', the average x-coordinate is \((3 + 9)/2 = 6\).
   • For E and E', the average x-coordinate is \((1 + 11)/2 = 6\).

   In all cases, the average x-coordinate equals 6.

3. Conclusion: Since all pairs of corresponding points line up with an average x-coordinate of 6, this indicates that the line of reflection responsible for the symmetry between the two polygons is the vertical line \(x = 6\).

Thus, the answer is Reflection across x = 6.