Use the image to determine the line of reflection.

Question

An image of polygon VWYZ with vertices V at negative 11, 2, W at negative 11, 0, Y at negative 5, 0, and Z at negative 5, 2. A second polygon V prime W prime Y prime Z prime with vertices V prime at 7, 2, W prime at 7, 0, Y prime at 1, 0, and Z prime at 1, 2.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = −2
Reflection across y = 2

Answer 1

To determine the line of reflection, we can compare the coordinates of the original polygon VWYZ and the reflected polygon V'W'Y'Z'.

1. Original Polygon VWYZ:

   • V(-11, 2)
   • W(-11, 0)
   • Y(-5, 0)
   • Z(-5, 2)

2. Reflected Polygon V'W'Y'Z':

   • V'(7, 2)
   • W'(7, 0)
   • Y'(1, 0)
   • Z'(1, 2)

We can analyze the difference in the x-coordinates for corresponding points:

• For points V and V':

  • V: (-11, 2) → V': (7, 2)
  • The x-coordinates change from -11 to 7. The midpoint between -11 and 7 is: \[ \text{Midpoint} = \frac{-11 + 7}{2} = \frac{-4}{2} = -2 \]
  • The line of reflection is at x = -2 for these points.

• For points W and W':

  • W: (-11, 0) → W': (7, 0)
  • The midpoint is again x = -2.

• For points Y and Y':

  • Y: (-5, 0) → Y': (1, 0)
  • The midpoint is also x = -2.

• For points Z and Z':

  • Z: (-5, 2) → Z': (1, 2)
  • The midpoint is again x = -2.

In every case, the reflection across the line \(x = -2\) holds true for all pairs of corresponding vertices.

Conclusion: The line of reflection is x = -2.