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An octagon is plotted in quadrant 2 of a coordinate plane. The coordinates of each vertex are labeled. (-3.4,6) (-2,6) (-1,5) (-4.4,5) (-4.4,3.6) (-3.4, 2.6) (-2, 2.6) (-1, 3.6)

The polygon shown has a line of reflection that will cause the figure to carry onto itself. Complete the equation for the vertical line of reflection.

(1 point)
The vertical line of reflection of the polygon is the equation x=
.

1 answer

To determine the vertical line of reflection for the octagon, we need to find the line that bisects the octagon symmetrically.

Given the coordinates:

  • (-3.4, 6)
  • (-2, 6)
  • (-1, 5)
  • (-4.4, 5)
  • (-4.4, 3.6)
  • (-3.4, 2.6)
  • (-2, 2.6)
  • (-1, 3.6)

We can calculate the average x-coordinate of the vertices to find the line of reflection. The x-coordinates are:

  • -3.4
  • -2
  • -1
  • -4.4
  • -4.4
  • -3.4
  • -2
  • -1

Now, let's sum these values:

\[ -3.4 + (-2) + (-1) + (-4.4) + (-4.4) + (-3.4) + (-2) + (-1) = -22 \]

There are 8 vertices, so the average x-coordinate is:

\[ \text{Average} = \frac{-22}{8} = -2.75 \]

The vertical line of reflection, which is equidistant from the leftmost and rightmost points of the polygon, will be:

\[ x = -2.75 \]

Thus, the final answer is:

The vertical line of reflection of the polygon is the equation \( x = -2.75 \).