Question

a segment is translated using the translation $(x,y)\to(x + 4,y + 8)$. what is the slope of the reflection line that would produce a glide reflection of the segment?
$m =$

Explanation:

Step1: Recall the property of glide reflection

In a glide reflection, the direction of the translation is perpendicular to the reflection line.

Step2: Find the slope of the translation vector

The translation vector is \((4,8)\). The slope of the translation vector is \(m_{translation}=\frac{8}{4} = 2\).

Step3: Find the slope of the reflection line

If two lines are perpendicular, the product of their slopes is \(- 1\). Let the slope of the reflection line be \(m\). Then \(m\times2=-1\). Solving for \(m\), we get \(m =-\frac{1}{2}\).

Answer:

\(-\frac{1}{2}\)