Question

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.

Explanation:

Step1: Find the mid - point of the horizontal distance between symmetric points

For a vertical line of reflection, we can consider the x - coordinates of symmetric points. Let's take the pair of points (-4, 1) and (-2, 1). The formula for the mid - point of two points $(x_1,y_1)$ and $(x_2,y_2)$ for the x - coordinate is $x=\frac{x_1 + x_2}{2}$. Here, $x_1=-4$ and $x_2=-2$.
$x=\frac{-4+( - 2)}{2}$

Step2: Calculate the value of x

$x=\frac{-4 - 2}{2}=\frac{-6}{2}=-3$

Answer:

$x = - 3$