To find the line of reflection for the given polygon that results in the figure carrying onto itself, we can look for the vertical line that is equidistant from the corresponding points.
Let's analyze the x-coordinates of the points you've provided:
- Point 1: (-3.4, 6)
- Point 2: (-4.4, 5)
- Point 3: (-4.4, 3.6)
- Point 4: (-3.4, 2.6)
- Point 5: (-2, 2.6)
- Point 6: (-1, 3.6)
- Point 7: (-1, 5)
- Point 8: (-2, 6)
Now we can identify pairs of points that are reflections of each other with respect to a vertical line. By checking the symmetry, we see:
- Points (-3.4, 6) and (-2, 6) are equidistant from the line x = -2.7.
- Points (-4.4, 5) and (-1, 5) are equidistant from the line x = -2.2.
- Points (-4.4, 3.6) and (-1, 3.6) are also equidistant, again from x = -2.2.
- Points (-3.4, 2.6) and (-2, 2.6) are equidistant from the line x = -2.7.
- Points (-2, 2.6) and (-2, 6) already align vertically (same x-coordinate).
After checking these points, we determine the average of the x-values from various symmetric pairs, leading us to:
For pairs (-4.4, 5) and (-1, 5), the midpoint x-coordinate reflects to: \[ \frac{-4.4 + (-1)}{2} = \frac{-5.4}{2} = -2.7. \] And for (-4.4, 3.6) and (-1, 3.6): \[ \frac{-4.4 + (-1)}{2} = -2.7. \]
Both of these calculations lead to the same line approximately x = -2.7.
Thus, the vertical line of reflection of the polygon that results in the figure carrying onto itself is: \[ \text{x = -2.7}. \]