In this problem, you are asked to find the slope of the line of reflection that would map the pink figure onto the blue figure.

Key Information:

1. The slope of one of the dotted lines is given as $\frac{3}{2}$.
2. The line of reflection will be perpendicular to the dotted lines connecting corresponding points on the pink and blue figures.

Steps:

• The line of reflection must be perpendicular to the dotted lines. If a line has slope $m$, then the slope of a line perpendicular to it will be $-\frac{1}{m}$.
• The slope of the dotted line is $\frac{3}{2}$, so the slope of the line of reflection will be: $-\frac{1}{\frac{3}{2}} = -\frac{2}{3}$

Thus, the slope of the line of reflection is $-\frac{2}{3}$.

Would you like further clarification or details?

Here are 5 questions to expand on this topic:

1. How do you find the equation of the reflection line if you are given a specific point on it?
2. What is the general rule for reflections over a line with a given slope?
3. How can you verify if a reflection has been performed correctly on a coordinate plane?
4. What transformations can result in the same figure orientation as a reflection?
5. How do the slopes of parallel and perpendicular lines relate in geometry?

Tip: When dealing with perpendicular lines, always remember their slopes are negative reciprocals of each other.