Question

Reflect the shape below across the line x = -2. Label the new coordinates

Answer 1

By definition, the reflection of the point P(x,y) in the line x = a is the point P'(-x+2a,y).

`\begin{gathered} \text{ line }x=a \\ P(x,y)\rightarrow P^(\prime)(-x+2a,y) \end{gathered}`

So, in this case, you have

`\begin{gathered} \text{ Line }x=-2 \\ \text{ Then a=-2} \end{gathered}`

And the transformation rule will be

`\begin{gathered} P(x,y)\rightarrow P^(\prime)(-x+2(-2),y) \\ P(x,y)\rightarrow P^(\prime)(-x-4,y) \end{gathered}`

Now, the coordinates of the image points will be

`p(-4,4)\rightarrow p´(-(-4)-4,4)=p´(4-4,4)=p´(0,4)`
`q(0,5)\rightarrow q^(\prime)(-0-4,5)=q^(\prime)(-4,5)`
`r(-6,-2)\rightarrow r^(\prime)(-(-6)-4,-2)=r^(\prime)(6-4,-2)=r^(\prime)(2,-2)`

Graphically you have