Question

1. write a reflection rule that maps each triangle to its image.

a. j(1, 0), k(-5, 2), l(4, -4) and j(-9, 0), k(-3, 2), l(-12, -4)
enter your answer.

Explanation:

Step1: Analyze x - coordinate changes

For point $J(1,0)$ and $J'(-9,0)$, the x - coordinate changes from $1$ to $-9$. For point $K(-5,2)$ and $K'(-3,2)$, the x - coordinate changes from $-5$ to $-3$. For point $L(4,-4)$ and $L'(-12,-4)$, the x - coordinate changes from $4$ to $-12$. The y - coordinates remain the same for all corresponding points.

Step2: Find the line of reflection

The mid - point between a point and its image for the x - coordinates gives the line of reflection. For $J(1,0)$ and $J'(-9,0)$, the mid - point of the x - coordinates is $\frac{1+( - 9)}{2}=\frac{1 - 9}{2}=-4$. The line of reflection is $x = - 4$. The reflection rule for a point $(x,y)$ across the line $x = a$ is $(2a - x,y)$. Here $a=-4$, so the rule is $( - 8 - x,y)$.

Answer:

$(x,y)\to(-8 - x,y)$