Question

given △xyz, line n with the equation x = - 2, and line p with the equation x = 2, write a translation that is equivalent to r_n ∘ r_p.

Explanation:

Step1: Find the distance between the two lines

The line $n$ has the equation $x = - 2$ and line $p$ has the equation $x=2$. The distance between two vertical lines $x = a$ and $x = b$ is given by $|b - a|$. Here, $a=-2$ and $b = 2$, so $|2-(-2)|=4$.

Step2: Determine the translation

A composition of two reflections $r_n\circ r_p$ over two parallel vertical lines $x=-2$ and $x = 2$ is equivalent to a translation. The translation is a horizontal translation. Since the distance between the two lines is 4, the translation vector is $\langle4,0
angle$.

Answer:

$\langle4,0
angle$