what is the equation for the line of reflection?

Explanation:

Step1: Identify mid - points of corresponding points

Find the mid - points of pairs of corresponding points (e.g., between A and A', B and B', etc.). The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For point A(2,2) and A'(10,2), the mid - point is $(\frac{2 + 10}{2},\frac{2+2}{2})=(6,2)$. For point B(6,3) and B'(6,3), the mid - point is (6,3). For point C(5,1) and C'(7,1), the mid - point is $(\frac{5 + 7}{2},\frac{1+1}{2})=(6,1)$. For point D(4,1) and D'(8,1), the mid - point is $(\frac{4 + 8}{2},\frac{1+1}{2})=(6,1)$.

Step2: Determine the line of reflection

The set of mid - points of corresponding points lie on the line of reflection. Since all the mid - points have an x - coordinate of 6, the equation of the line of reflection is a vertical line with the equation $x = 6$.

Answer:

$x = 6$