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.

Answer 1

To determine the equation of the vertical line of reflection for a polygon that will map onto itself, you typically need to find the midpoint of the top and bottom points of the polygon along the vertical axis, or alternatively, the line of symmetry.

A vertical line of reflection is expressed in the form $x=k$, where $k$ is a constant representing the x-coordinate.

1. Identify the polygon: Examine the vertices of the polygon if they are given. This will help you understand the shape and position of the polygon in the coordinate plane.

2. Find the midpoint: If the polygon is symmetric in the x-axis, you would take the x-coordinates of the leftmost and rightmost vertices and find their average.

For example, if the leftmost point has an x-coordinate of $x_1$ and the rightmost point has an x-coordinate of $x_2$, the line of reflection $x=k$ would be determined by: $$k=\frac{x_1+x_2}{2}$$

3. Write the equation: Plug the value of $k$ into the equation form $x=k$.

If you provide specific coordinates or additional details about the polygon, I could give you a more precise answer.