The point A (7, 6) is reflected about the line x = 3, then about the line x = k. The final image is A”(5, 6). What is the value of k?

Answer 1

reflection about x=3 takes (x,y) -> (3-x,y)
reflection about x=k takes (x,y) -> (k-x,y)
So, both reflections take
(x,y)->(3-x,y)->(k-(3-x),y) = (k-3+x,y)

So, since (7,6)->(5,6)
k-3+7 = 5
k=1