Question

1. given the image on the left, what is the equation for the line of reflection?

Explanation:

Step1: Analyze the symmetry

For a vertical line of reflection \(x = a\), the distance from each point of the pre - image to the line \(x=a\) is equal to the distance from the corresponding point of the image to the line \(x = a\).
Let's take a point from the pre - image. Suppose a point on the pre - image has an \(x\) - coordinate \(x_1\) and the corresponding point on the image has an \(x\) - coordinate \(x_2\). The formula for the line of reflection \(x=a\) is \(a=\frac{x_1 + x_2}{2}\).
Looking at the graph, if we consider the horizontal alignment of the pre - image and image. The pre - image is on the right side and the image is on the left side.

Step2: Determine the line of reflection

Since the reflection is a vertical line (because the left - right orientation of the pre - image and image is reversed while the up - down orientation is related by a vertical - line reflection).
By visual inspection (or by using the mid - point formula for \(x\) - coordinates of corresponding points), we can see that the line \(x = 2\) is the line of reflection.

Answer:

\(x = 2\)