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Use the image to answer the question.

Hexagon upper W (-n,0)
upper X (n,0)
upper Y(?,?)
upper Z(?,?)
upper U(?,-k)
upper V(-m,-r)
is plotted in quadrants 3 and 4 of an unmarked coordinate plane. The coordinates of each vertex are labeled.

Refer to the polygon in the diagram. Identify a line of reflection that flips the polygon onto itself.

(1 point)
Responses

x=−m
x equals negative m

x=n
x equals n

y=0
y equals 0

y=−r

1 answer

To find a line of reflection that flips the polygon onto itself, we first consider the coordinates of the vertices given:

  • W (-n, 0)
  • X (n, 0)
  • U (?, -k)
  • V (-m, -r)

Given that the polygon is plotted in quadrants 3 and 4, the most apparent line of reflection that produces symmetry across the vertical axis would be the y-axis (x = 0). However, the options provided suggest we need to think about specific values related to the coordinates of the vertices.

Among the options:

  1. x = -m - This line would reflect points around the vertical line through -m.
  2. x = n - This line would reflect points around the vertical line through n.
  3. y = 0 - This is the x-axis line; reflecting over this would not maintain the polygon's position in quadrants 3 and 4.
  4. y = -r - This is a horizontal line; depending on the value of r, but does not align with a typical axis of symmetry for the given coordinates.

Given that points W and X have symmetrical x-coordinates around the y-axis, and considering the standard symmetry in polygons, the best line of reflection for maximum symmetry would typically be the y-axis itself or a similar approach. However, we need to select from the provided options.

Since the question is looking for a line of reflection that maintains the vertices in quadrants 3 and 4 and leads to symmetry across the y-axis, the best option from the list provided would be:

y = 0

This choice reflects the polygon horizontally, maintaining a structure for reflection across the horizontal axis. Thus, the correct answer is:

y = 0.