Question 622465
After a reflection in the line y=x, (-8,-3) is the image of point Q. What is the original location of point Q? _____
<pre>
We draw the point (-8,-3) and the line y=x  (in green).  That line
goes 45° through the origin.  It is called the IDENTITY line, because
its equation x=y says x and y are IDENTICAL.

{{{drawing(400,400,-12,12,-12,12, graph(400,400,-12,12,-12,12),
circle(-8,-3,.1), locate(-8,-2,"(-8,-3)"),

green(line(40,40,-40,-40)) )}}}

If the green line y=x were a mirror, the reflection of the point
(-8,-3) would reflect like the dotted line shows:

{{{drawing(400,400,-12,12,-12,12, 
circle(-8,-3,.1), locate(-8,-2,"(-8,-3)"),
graph(400,400,-12,12,-12,12,

(-x-11)*sqrt(sin(10x))/sqrt(sin(10x))*sqrt(x+8)/sqrt(x+8)*sqrt(-x-3)/sqrt(-x-3)

), circle(-3,-8,.1), locate(-6.5,-8,"(-3,-8)"),

green(line(40,40,-40,-40)) )}}}

That point is the INVERSE point (-3,-8).  Notice that any time you
reflect a point into the line y=x, you get the point with the x and y
coordinates switched, called the INVERSE point.  You should find that interesting!

Edwin</pre>