How to Reflect a Shape in y = x Using Cartesian Coordinates
Reflecting a Shape in y = x Using Cartesian Coordinates
A shape can be reflected in the line y = x.
If point on a shape is reflected in the line y = x, the xcoordinate becomes the ycoordinate and the ycoordinate becomes the xcoordinate.
The image below shows a point on a shape being reflected in the line y = x:

The point A has Cartesian coordinates (2, 3).

The reflected point A' has Cartesian coordinates (3, 2).
The xcoordinate of A (2) has become the ycoordinate of A'. The ycoordinate of A (3) has become the xcoordinate of A'.
How to Reflect a Shape in y = x Using Cartesian Coordinates
Reflecting a shape in the line y = x using Cartesian coordinates is easy.
Question
Reflect the shape below in the line y = x.
StepbyStep:
1
Find the Cartesian coordinates of each point on the shape.
Write the xcoordinates and ycoordinates of each point.
Point  xcoordinate  ycoordinate 

A  1  6 
B  4  5 
C  1  4 
2
Find the Cartesian coordinates of the reflected points.
Swap the xcoordinate and the ycoordinate of the original point.
Point  xcoordinate  ycoordinate  Point  xcoordinate  ycoordinate 

A  1  6  A'  6  1 
B  4  5  B'  5  4 
C  1  4  C'  4  1 
3
Plot the reflected points and draw in the shape.
Answer:
We have reflected the shape in the line y = x.
A Formula to Reflect a Point in y = x Using Cartesian Coordinates
In general, we write Cartesian coordinates as:
x is the xcoordinate. y is the ycoordinate. x and y can taken any number.
The reflected point has Cartesian coordinates:
The image below shows a general Cartesian coordinate being reflected in the line y = x: