The point P (3,4)is reflected to p' in the x-axis and O' is the image of O (the origin ) in the line PP' . Find

P' is (3,-4) which is the image of P 

Now image of origin in line PP' which is x = 3 is O'

O' = (3+3,0) = (6,0)

Now it can be easily seen that all the sides of the quadrilateral = 5

So it is a rhombus .