transformations **moving a point on a coordinate plane
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TransformationsTransformations
**Moving a point on a coordinate plane**Moving a point on a coordinate plane
TransformationsTransformations - Moving a point on a coordinate - Moving a point on a coordinate planeplane
Line SymmetryLine Symmetry – an object is symmetric about a line – an object is symmetric about a line
♂List the upper case letters of the alphabet that have line symmetry
Line ReflectionLine ReflectionA
B
C
A’
B’
C’
'AArl
'BBrl
'CCrl
Properties preserved:
'' - Distance BAAB
'' ofmidpoint theis ' -
ofmidpoint theis -Midpoint
BAD
ABD
D’D
The preimage of A’ is A
Notation:
rl(ABC)→A’B’C’
-Equal distance from the line of reflection Equal distance from the line of reflection - Perpendicular to the line of reflectionPerpendicular to the line of reflection
NORIENTATIO - PreservedNot
Clockwise -Counter - C'B'A'
Clockwise - ABC
l
2. Tell which of the following words have line symmetry. If 2. Tell which of the following words have line symmetry. If line symmetry exists, draw the line(s).line symmetry exists, draw the line(s).
a. DAD b. MOM c. HIKED d. CHECK
e. BOB f. DEED g. RADAR h. CHOKE
i. AVA j. TOOT k. AXIOM l. YOUTH
In 4-10, the reflection of Triangle ABC in line In 4-10, the reflection of Triangle ABC in line k k is is triangle DECtriangle DEC
A
B
C
D
E
4. What is the image of point A under the line reflection?
D
?)( 5. k Br ?)( 6. k Cr ?)( 7. k DrE C A
8. What is the preimage of point B under the line reflection?
E
?)( 9. k ABCr
DEC?)( 10. k DEr
AB
k
In 11-24, draw lines of symmetry for each of the In 11-24, draw lines of symmetry for each of the figuresfigures
11. 12. 15.
17.18. 19.
20. 24.
1. Under a reflection in the x-axis, the image of (x,y) is __________
2. Under a reflection in the y-axis, the image of (x,y) is __________
3. Under a reflection in the line y=x, the image of (x,y) is __________
(-2,4)
(-2,-4)
(2,4)
(4,-2)
),( yx
),( yx
),( xy
Remember the following Rules:
These are the first three rules that you are to remember.
HomeworkHomework Page 2: 4-16 evenPage 2: 4-16 even
Find the image of the point under a reflection in the x-axis
4. (5,7) 6. (-1,-4)
)7,5(
)7,5(
)4,1(
)4,1(
)7,5( )4,1(
Find the image of the point under a reflection in the y-axis
8. (5,7) 10. (0,6)
)7,5()7,5()6,0(
)7,5( )6,0(
Find the image of the point under a reflection in the line y=x
12. (5,7) 14. (0,-2)
)7,5(
)5,7(
)2,0(
)5,7( )0,2(
)0,2(
16. Using the rule (x,y)→(x,-y), find the images of C(1,4), A(5,1), and T(4,5), namely C’, A’, T’.
)5,4(
)1,5(
)4,1(
),(),(
T
A
C
yxyx
)5,4('
)1,5('
)4,1('
T
A
C
CA222 cba 222 43 c
2169 c225 c 225 c
c5
''AC222 43 c
2169 c225 c 225 c
c5
'' ACCA Distance is preserved under the given
transformation.
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