Use the image to answer the question.

Question

An octagon is plotted in quadrant 2 of a coordinate plane. The coordinates of each vertex are labeled.
(-3.4,6)
(-4.4,5)
(-4.4,3.6)
(-3.4,2.6)
(-2,6)
(-1,5)
(-1.3,6)
(-2.2,6)
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=

Answer 1

To find the vertical line of reflection for the octagon, we need to find the x-coordinate that is equidistant from the x-coordinates of the vertices of the shape when they are reflected.

The x-coordinates of the vertices are:

• -3.4
• -4.4
• -4.4
• -3.4
• -2
• -1
• -1.3
• -2.2

The maximum x-coordinate in the polygon is -1 (from the vertices (-1, 5) and (-1.3, 6)), and the minimum is -4.4 (from the vertices (-4.4, 5) and (-4.4, 3.6)).

To find the vertical line of reflection, we can use the formula for finding the midpoint between the leftmost and rightmost x-coordinates.

1. Identify the leftmost and rightmost x-coordinates:

   • Leftmost: -4.4
   • Rightmost: -1

2. Find the midpoint: \[ x = \frac{-4.4 + (-1)}{2} = \frac{-5.4}{2} = -2.7 \]

Thus, the equation for the vertical line of reflection is: \[ \text{x = -2.7} \]

So, the complete sentence would be: The vertical line of reflection of the polygon is the equation x = -2.7.