SECTION 7.5REFLECTIONS AND LINESYMMETRY
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REFLECTIONS
A flip/transformation in a mirror line (reflection line)
Objects reflected over a mirror line will look symmetrical
Mirror Line
Object
Image
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LINE OF SYMMETRY
A line that divides an image in half
Both sides of the image look the same over the line(symmetrical)
IMAGE
Line of Symmetry
Everything on theleft side of the
line of symmetry
is equal to everything
on the right side ofthe line of symmetry
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EXAMPLES OF SYMMETRY IN ART
Cup or faces paradox
Paintings, Grafiti
Architecture: Taj Mahul, Acropolis
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EX: DRAW THE LINES OF SYMMETRY FOR EACH OF THE FOLLOWINGSHAPES
3 lines ofsymmetry
5 lines ofsymmetry
4 lines ofsymmetry
NO lines ofsymmetry
1 line ofsymmetry
Any line that goes throughthe center is a line of symmetry
Infinite # oflines of symmetry
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EX: GRAPH EACH IMAGE OVER THE LINE OF SYMMETRY.
D
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III) TYPES OF REFLECTIONS
Horizontal Reflections
Image is reflected sideways (left/right)
Reflected over the Y-axis or any vertical line
Vertical Reflection
Image is reflected upside down
Reflected over the X-axis orany horizontal line
Diagonal Reflection
Image is reflected over a slantedline at y=x
Up Right, Down left
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
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EX: GIVEN FOLLOWING DIAGRAM, DRAW THE IMAGE AFTERTHE REFLECTION OVER THE X-AXIS. LABEL THE COORDINATESOF THE IMAGE:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
Objects reflected over theline of symmetry will beequal distances from it
After the image is drawn,find the coordinates ofeach vertex
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EX: GIVEN FOLLOWING DIAGRAM, DRAW THE IMAGE AFTERTHE REFLECTION OVER THE LINE X=1. LABEL THECOORDINATES OF THE IMAGE:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
The line x = 1 is a verticalline with a x-intercept of 1
Reflect each vertex overthe line of reflection
After the image is drawn,find the coordinates ofeach vertex
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EX: GIVEN FOLLOWING DIAGRAM, DRAW THE IMAGE AFTERTHE REFLECTION OVER THE LINE Y=X. LABEL THECOORDINATES OF THE IMAGE:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
Objects pointing up willbe reflected to the right
Objects pointing down willbe reflected to the left
After the image is drawn,find the coordinates ofeach vertex
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HOMEWORK:
P358 #5, 7 – 9, 11
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