Reflection In 2D Graphics

Reflection deals with obtaining a mirror image of the 2D object. 

About x-axis:
If P(x, y) is the point on x-y plane then P’(x’, y’) is the reflection about x-axis given as x’=x ; y’=-y 

Matrix Form: 

About y-axis :
If P(x, y) is the point on x-y plane then P’(x’, y’) is the reflection about y-axis given as x’=-x ; y’=y 

Along origin :
If P(x, y) is the point on x-y plane then P’(x’, y’) is the reflection about origin given as x’=-x ; y’=-y 

About x=y line : To do this move x=y line to any of the axis. In the given diagram the angle of rotation is 45^o as the points are plotted as (0, 0), (1, 1), (2, 2), and so on. 

Imposing the line clockwise (-45^o) imposing it on the x-axis we have, 

We know, 

and 

Now perform reflection along x-axis, 

Now rotate the line back 45^o in an anticlockwise direction, 

Now if P(x, y) is the point on x-y plane then P’(x’, y’) is the reflection about x=y line given as x’=y ; y’=x  
Matrix Form: 

Problem: A triangle is given with the coordinates p (5 4), q (2 2), r (5 6) we need to reflect it along Y-axis.

Ans: We are given with coordinate p, q, r as shown in figure-

Triangle reflection in 2-d graphics

Now, we apply the condition of reflecting a 2-d object along Y-axis:

First coordinate p, becomes p’ after reflection:

Second coordinate q, becomes q’ after reflection:

Third coordinate r of the triangle becomes r’ after reflection:

After reflecting the triangle about the Y-axis point p, q, r becomes p’, q’, r’ :

p(5, 4) = p'(-5, 4) , q(2, 2) 
= q'(-2, 2) , r(5, 6) 
= r'(-5, 6) 

The reflecting object would appear as :