• An image that looks the same when turned 180º is said to have point symmetry.
• (the point of symmetry is the center of the shape) yes No Yes No
List the upper case letters of the alphabet that have point symmetry.
H I N O S X Z

– reflecting an image about a point
Notation: R origin
(A)→A’
In 3-9, the reflection of triangle ABC through point
B is triangle DBE.
3. What is the image of A under the point reflection?
D
4 .
R
B
( C )
E

?
5 .
R
B
( D )
A

?
7. What is the preimage of C under the point reflection?
E
6 .
R
B
( B )
B

?
C
A
B
8 .
R
B
(

CAB )

EDB

?
9 .
R
B
( CA )

?
ED
D
E

In 10-18: Sketch the figure. Tell whether the figure has point symmetry. If it does locate the point.
14.
15.
12.
16.
13.
17.
18.

In 19-22: Sketch the figure. Carefully sketch the given figure under a reflection in point A.
B
D
C
C A
A’
C’
B’
A
A’
B
C’
B’
D’

Reflect the image of AB with endpoints A(-6,3), B(3,1) through the origin.
( x , y )

(?, ?)
A
B
(

6 ,
( 3 ,
3 )

1 )

A ' ( 6 ,

3 )
B ' (

3 ,

1 )
A (

6 , 3 )
( x
origin
, y )

(
 x ,
 y )
B ' (

3 ,

1 )
B ( 3 , 1 )
A ' ( 6 ,

3 )

In 2-5, find the image of the point under a reflection in the origin.
3 .
(

7 , 1 )

R
  
( 7 ,

1 )
5 .
(

3 , 0 )

R
  
( 3 , 0 )
B ' ( 3 , 0 )
A ' ( 7 ,

1 )

7a) Using the rule (x,y) → (-x,-y), find the images of A(-5,-2),
B(-1,-2), C(-1,4), and D(-3,3), namely A’, B’, C’, D’.
( x , y )

(
 x ,
 y )
A (

5 ,

2 )

A ' ( 5 , 2 )
B (

1 ,

2 )

C (

1 , 4 )

B
C
'
'
(
(
1 ,
1 ,
2

)
4 )
D (

3 , 3 )

D ' ( 3 ,

3 ) b) On one set of axes, draw quadrilateral ABCD and
A’B’C’D’
You can check by extending a line from A to A’ through the origin
B '
C '
D '
A '

In 2-5, find the image of the point under a reflection in the origin.
2 .
( 6 ,

3 )

R
  
(

6 , 3 )
4 .
( 0 , 0 )

R
  
( 0 , 0 )
A '
B '
A

6a) Using the rule (x,y) → (-x,-y), find the images of A(2,1),
B(4,5), C(-1,3), namely A’, B’, C’.
( x , y )

(
 x ,
 y )
A ( 2 , 1 )

B ( 4 , 5 )

A
B '
'
(
(


2
4 ,
,


1 )
5 )
C (

1 , 3 )

C ' ( 1 ,

3 ) b) On one set of axes, draw triangles ABC and A’B’C’.
A '
C '
B '

8a) Draw triangle RST whose vertices are R(-2,-1), S(-2,2),
T(4,2), namely R’, S’, T’.
b) Find the image of each of the vertices, namely R’S’T’
( x , y )

(
 x ,
 y )
R (

2 ,

1 )

S (

2 , 2 )

T ( 4 , 2 )

R ' ( 2 , 1 )
S ' ( 2 ,

2 )
T ' (

4 ,

2 ) c) On one set of axes, draw triangles RST and R’S’T’.
R '
S '
T '