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