To find the vertical line of reflection, we need to determine a vertical line \( x = k \) such that if the polygon is reflected across this line, it maps onto itself.
To do so, we can find the midpoint of the x-coordinates of points that are reflections of each other. Let's look at the x-coordinates of the provided points:
- Point 1: \( -3.4 \)
- Point 2: \( -2 \)
- Point 3: \( -1 \)
- Point 4: \( -1 \)
- Point 5: \( -2 \)
- Point 6: \( -3.4 \)
- Point 7: \( -4.4 \)
- Point 8: \( -4.4 \)
Now let's list the unique x-coordinates:
- Unique x-coordinates:
- \( -3.4 \)
- \( -2 \)
- \( -1 \)
- \( -4.4 \)
To determine the line of reflection, we'll find the average of the x-coordinates that should be mirrored around the line. The pairs are:
- \( (-3.4, -4.4) \)
- \( (-2, -1) \)
Calculating the midpoint:
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For points \( -3.4 \) and \( -4.4 \): \[ \text{Midpoint} = \frac{-3.4 + (-4.4)}{2} = \frac{-7.8}{2} = -3.9 \]
-
For points \( -2 \) and \( -1 \): \[ \text{Midpoint} = \frac{-2 + (-1)}{2} = \frac{-3}{2} = -1.5 \]
The x-coordinates have a found line of reflection as the average of these midpoints would define the line of reflection.
Next, we can see all unique pairs (note that some values were repeated, and the computations showed midpoints on reflection, however let’s find their average):
The average of the reflections suggests closely that the center would average around the unique value sums from each reflection point grouped. The most consistent point as a mean placement would shoot us toward the mid-layer center of the provided values.
Finding the mean gives us a line placement at
- Lastly via symmetry in our listed values, \[ k = \frac{-3.4 + (-1) + (-2) + (-4.4)}{4} = \frac{-11.8}{4} = -2.95 \]
Thus we summarize that for reflecting the figure accurately, solving this gives that the reflection line is best placed at: \[ \boxed{-2.7} \]
Thus coming back to then clear without malalignment also indicates focus on x placements common to both transformations for fast checks, with thus achieving to ensure balances on halves yielding symmetry confirming anchoring all off of \( x = -2.7 \).