Use the graph to answer the question.

Question

Graph of polygon ABCDE with vertices at negative 3 comma 5, negative 3 comma 8, 1 comma 8, 1 comma 5, negative 1 comma 3. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma 5, 13 comma 8, 9 comma 8, 9 comma 5, 11 comma 3.

Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 5
Reflection across y = 6

Answer 1

To determine the line of reflection between polygon ABCDE and its reflected polygon A'B'C'D'E', we can analyze the coordinates of the corresponding vertices of both polygons.

1. Coordinates of polygon ABCDE:

   • A: (-3, 5)
   • B: (-3, 8)
   • C: (1, 8)
   • D: (1, 5)
   • E: (-1, 3)

2. Coordinates of polygon A'B'C'D'E':

   • A': (13, 5)
   • B': (13, 8)
   • C': (9, 8)
   • D': (9, 5)
   • E': (11, 3)

Next, we compare corresponding vertices to determine the line of reflection.

• For points A and A':
  • Midpoint of (-3, 5) and (13, 5) is ((-3 + 13)/2, (5 + 5)/2) = (5, 5)
• For points B and B':
  • Midpoint of (-3, 8) and (13, 8) is ((-3 + 13)/2, (8 + 8)/2) = (5, 8)
• For points C and C':
  • Midpoint of (1, 8) and (9, 8) is ((1 + 9)/2, (8 + 8)/2) = (5, 8)
• For points D and D':
  • Midpoint of (1, 5) and (9, 5) is ((1 + 9)/2, (5 + 5)/2) = (5, 5)
• For points E and E':
  • Midpoint of (-1, 3) and (11, 3) is ((-1 + 11)/2, (3 + 3)/2) = (5, 3)

From these calculations, we can see that the midpoints of the corresponding points all share the same x-coordinate of 5. This indicates that the line of reflection is a vertical line.

Given all this information, the line of reflection is x = 5.