Question 582417
What is the image of A(3,-1) after a reflection, first across the line y=3, and then across the line x=-1?
<pre>
First we plot the point A(3,-1) and the horizontal line y = 3 (in green)

{{{drawing(390,390,-8,5,-5,8,
graph(390,390,-8,5,-5,8), circle(3,-1,.08), locate(3.2,-.9,"A(3,-1)"),
green(line(-10,3,10,3)))}}} 

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) 

{{{drawing(390,390,-8,5,-5,8,
graph(390,390,-8,5,-5,8), circle(3,-1,.08), locate(3.2,-.9,"A(3,-1)"),
green(line(-10,3,10,3)),

graph(390,390,-8,5,-5,8), circle(3,7,.08), locate(3.2,7.1,"(3,7)"))}}} 

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

{{{drawing(390,390,-8,5,-5,8,
graph(390,390,-8,5,-5,8), circle(3,-1,.08), locate(3.2,-.9,"A(3,-1)"),
green(line(-10,3,10,3)),

blue(line(-1,-10,-1,10)),

graph(390,390,-8,5,-5,8), circle(3,7,.08), locate(3.2,7.1,"(3,7)"))}}}

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) 


{{{drawing(390,390,-8,5,-5,8,
graph(390,390,-8,5,-5,8), circle(3,-1,.08), locate(3.2,-.9,"A(3,-1)"),
green(line(-10,3,10,3)),

circle(-5,7,.08), locate(-4.8,7.1,"(-5,7)"),

blue(line(-1,-10,-1,10)), 

graph(390,390,-8,5,-5,8), circle(3,7,.08), locate(3.2,7.1,"(3,7)"))}}}

Answer: (-5,7)

Edwin</pre>