SOLUTION: What is the image of A(3,-1) after a reflection, first across the line y=3, and then across the line x=-1?

First we plot the point A(3,-1) and the horizontal line y = 3 (in green)

 

Now we pretend that the green line is a mirror facing the point.  Then
we draw where A's image would appear to be.  Since A is 4 units below
the green line, its image will be 4 units above the green line, at the
point (3,7) 

 

Now we draw the vertical line x = -1 (in blue)



Now we pretend that the blue line is a mirror facing the point (3,7).  
Then we draw a point where its image would appear to be.  Since (3,7) 
is 4 units to the right the blue line, its image will be 4 units to the
left of the blue line, at the point (-5,7) 




Answer: (-5,7)

Edwin