Use the graph to answer the question.

Question

Graph of polygon VWXYZ with vertices at 1 comma 2, 1 comma 0, 4 comma negative 7, 7 comma 0, 7 comma 2. A second polygon V prime W prime X prime Y prime Z prime with vertices at 1 comma negative 12, 1 comma negative 10, 4 comma negative 3, 7 comma negative 10, 7 comma negative 12.

Determine the line of reflection.
Reflection across the x-axis
Reflection across x = 4
Reflection across y = −5
Reflection across the y-axis

Answer 1

To determine the line of reflection between the two polygons, we can analyze the coordinates of the corresponding vertices of each polygon.

For polygon VWXYZ:

• \( V(1, 2) \)
• \( W(1, 0) \)
• \( X(4, -7) \)
• \( Y(7, 0) \)
• \( Z(7, 2) \)

For polygon \( V'W'X'Y'Z' \):

• \( V'(1, -12) \)
• \( W'(1, -10) \)
• \( X'(4, -3) \)
• \( Y'(7, -10) \)
• \( Z'(7, -12) \)

Now, to find the line of reflection, we first need to see how the y-coordinates of the vertices reflect.

1. For Point V and V':

   • V: (1, 2) reflects to V': (1, -12).
   • The midpoint is \((1, (2 + (-12))/2) = (1, -5)\).

2. For Point W and W':

   • W: (1, 0) reflects to W': (1, -10).
   • The midpoint is \((1, (0 + (-10))/2) = (1, -5)\).

3. For Point X and X':

   • X: (4, -7) reflects to X': (4, -3).
   • The midpoint is \((4, (-7 + (-3))/2) = (4, -5)\).

4. For Point Y and Y':

   • Y: (7, 0) reflects to Y': (7, -10).
   • The midpoint is \((7, (0 + (-10))/2) = (7, -5)\).

5. For Point Z and Z':

   • Z: (7, 2) reflects to Z': (7, -12).
   • The midpoint is \((7, (2 + (-12))/2) = (7, -5)\).

From this analysis, we can see that for all pairs of corresponding points, the midpoints consistently yield a y-coordinate of \(-5\). This indicates that the line of reflection is the horizontal line \(y = -5\).

Thus, the correct answer is:

Reflection across y = -5.