Question

slope of one of the dotted lines: $\frac{-2}{-5}$
slope of the line of reflection:

Explanation:

Step1: Recall the property of line - of - reflection and perpendicular lines

The line of reflection is perpendicular to the line segment connecting a point and its image. If two non - vertical lines are perpendicular, the product of their slopes is - 1.

Step2: Identify the slope of the dotted line

The slope of one of the dotted lines is given as $\frac{-2}{-5}=\frac{2}{5}$.

Step3: Calculate the slope of the line of reflection

Let the slope of the line of reflection be $m$. Since the line of reflection is perpendicular to the dotted line, we know that $m\times\frac{2}{5}=-1$. Solving for $m$, we get $m =-\frac{5}{2}$.

Answer:

$-\frac{5}{2}$