Question

What are the coordinates of images 2? For B P Q

Answer 1

Recall that a reflection over a line y=k transforms the point (x,y) into:

$(x,k-(y-k))=(x,2k-y)\text{.}$

Therefore the given sequence of transformations will change point (x,y) into:

$(x,y)\rightarrow(x+3,y-3)\rightarrow(x+3,2(-2)-(y-3))=(x+3,-1-y)\text{.}$

Answer:

Since the original coordinates are P(-4,3), Q(0,3), and B(-3,-1), the coordinates of image 2 are:

$\begin{gathered} P^{\doubleprime}(-4+3,-1-3)=P^{\doubleprime}(-1,-4), \\ Q^{\doubleprime}(0+3,-1-3)=Q^{\doubleprime}(3,-4), \\ B^{\doubleprime}(-3+3,-1-(-1))=B^{\doubleprime}(0,0)\text{.} \end{gathered}$