Question 949859
A reflection is a kind of transformation. It is basically a 'flip' of a shape over the line of reflection. Very often reflections are performed using coordinate notation because it allow us to easily describe the image and its pre-image.

Reflection in the {{{x}}}-axis.

 A reflection in the x-axis when {{{ A}}} is reflected to its image {{{A}}}' or {{{I}}} then point ({{{A}}},{{{B}}}) -> ({{{A}}}, {{{-B}}}) 
let it be points ({{{1}}},{{{2}}}) -> ({{{1}}},{{{ -2}}})

to remember it easier you just imagine x-axis is a mirror, point ({{{A}}},{{{B}}}) is like you standing in front of that mirror and you see your reflection in mirror, same is with a point ({{{A}}},{{{B}}}) whose reflection is ({{{A}}}, {{{-B}}}) 


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(1,2,.12), circle(1,-2,.12),
locate(1,2,A(1,2)),locate(1,-2,I(1,-2)),
 graph( 600, 600, -10, 10, -10, 10, 0)) }}} 


A reflection in the y-axis when  {{{A}}} is reflected to its image {{{A}}}' or {{{I}}} then point ({{{A}}},{{{B}}}) -> ({{{-A}}}, {{{B}}}) 

using a point ({{{3}}},{{{4}}}) , we have

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(3,4,.12), circle(-3,4,.12),
locate(3,4,A(3,4)),locate(-3,4,I(-3,4)),
 graph( 600, 600, -10, 10, -10, 10, 0)) }}} 


A reflection in the line {{{y = x}}} when  {{{A}}} is reflected to its image {{{I}}} then point ({{{A}}},{{{B}}}) -> ({{{B}}},{{{A}}} )

if we use same point ({{{3}}},{{{4}}}) , we have

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(3,4,.12), circle(4,3,.12),
locate(3,4,A(3,4)),locate(4,3,I(4,3)),
 graph( 600, 600, -10, 10, -10, 10, x)) }}}