Question

This image features a coordinate plane with a symmetrical octagon plotted in the second quadrant. Each vertex is marked with a black dot and labeled with coordinates, which are as follows:

(-3.4, 6)

(-2, 6)

(-1, 5)

(-1, 3.6)

(-2, 2.6)

(-3.4, 2.6)

(-4.4, 3.6)

(-4.4, 5)

The orange lines connect these vertices, forming the octagon. The grid spans from -6 to 6 on both the x-axis and y-axis, with intervals of 1 unit between grid lines.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=
.

Answer 1

To find the vertical line of reflection for the symmetrical octagon given the coordinates of its vertices, we can look for the midpoint along the horizontal (x) axis of the two symmetrical points.

We can analyze the x-coordinates of the vertices:
- The x-coordinates are: -3.4, -2, -1, -1, -2, -3.4, -4.4, -4.4.

To find the line of symmetry, we can check the x-coordinates of the leftmost and rightmost points:
- The largest x-coordinate is -1 and the smallest x-coordinate is -4.4.

The vertical line of reflection is the x-coordinate that is equidistant from the leftmost and rightmost vertices. To find this line of symmetry, we will calculate the average of these two x-coordinates:

\[
\text{Average} = \frac{x_1 + x_2}{2} = \frac{-1 + (-4.4)}{2} = \frac{-5.4}{2} = -2.7.
\]

Thus, the equation for the vertical line of reflection is:

\[
\text{x} = -2.7.
\]

So the complete answer is:

The vertical line of reflection of the polygon is the equation \( x = -2.7 \).