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

Question

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

Y=-r
X=-m
Y=0
X=n

Answer 1

To determine a line of reflection that flips the polygon onto itself, we need to understand the properties of the polygon and its vertices based on the coordinates provided.

1. Reflection in a Horizontal Line:
   If the polygon is symmetric about a horizontal line, that line would typically reflect points vertically. Given the point coordinates W(-n,0), X(n,0), and assuming other points are symmetrically placed, a potential line of reflection could be \( y = 0 \) (the x-axis).

2. Reflection in a Vertical Line:
   If the polygon is symmetric about a vertical line, that line would typically reflect points horizontally. In this case, given coordinates W and X are along the x-axis but negative and positive, respectively, a vertical line like \( x = 0 \) (the y-axis) might also be a line of reflection.

3. Based on your selections:

   • Y = -r: This could be a line below the x-axis, which may not flip the polygon onto itself unless specific points exist at that position.
   • X = -m: This could be a reflection if the polygon has symmetry around this line.
   • Y = 0: This reflects points above and below the x-axis. It can flip W and X onto themselves.
   • X = n: This doesn't seem to create symmetry as it would more likely displace points to the left rather than reflecting correctly.

Given the coordinates, lines having the same distances on either side would yield a reflection. The most fitting option based on standard geometric reasoning for flipping the points symmetrically would be:

Line of Reflection: Y = 0 (The x-axis)

This line will reflect the entire polygon, keeping points like W and X in their respective positions and flipping points in the y-direction accordingly, creating symmetry.