Basic Examples 
(2)
 

Reflect points about a given line:
mirror2={{3,2},{2,-1}};​​pts2=Subsets[Range[0,4],{2}];
ref=
[◼]
ReflectPoints
[mirror2,pts2]

24
5
,-
3
5
,
27
5
,
1
5
,{6,1},
33
5
,
9
5
,
23
5
,
4
5
,
26
5
,
8
5
,
29
5
,
12
5
,
22
5
,
11
5
,{5,3},
21
5
,
18
5

Graphics[{Point[pts2],{Green,InfiniteLine[mirror2]},{Red,Point[ref]}}]
Out[1372]=
———
Reflect points about a given plane:
mirror3={{3,2,0},{2,-1,0},{1,1,1}};​​pts3=Subsets[Range[0,4],{3}];
ref=
[◼]
ReflectPoints
[mirror3,pts3]
-
12
35
,
39
35
,
10
7
,-
6
5
,
7
5
,1,-
72
35
,
59
35
,
4
7
,-
36
35
,
82
35
,
9
7
,-
66
35
,
92
35
,
6
7
,-
12
7
,
25
7
,
8
7
,-
19
35
,
88
35
,
3
7
,-
7
5
,
14
5
,0,-
43
35
,
131
35
,
2
7
,-
26
35
,
137
35
,-
4
7

Graphics3D[{Point[pts3],{Green,InfinitePlane[mirror3]},{Red,Point[ref]}},Lighting"Standard"]

Scope 
(2)
 
