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Reflections
GeometryUnit 7, Lesson 1Mrs. King
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BrainPop!
http://www.brainpop.com/math/geometryandmeasurement/transformation/preview.weml
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What is a Reflection?
Definition:A flip.
Example?
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How to do a Reflection
1. Plot the point(s).
2. Count from the point to the line of reflection.
3. Count the same number of spaces in the opposite direction.
4. Plot the image.
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Graphing Coordinates Plot the point A(4,6). Reflect the point
(4,6) over the x-axis. Label this point A’ and state the coordinates.
Reflect the point (4,6) over the y-axis. Label this point A” and state the coordinates.
y
x
10
10
-10
-10
A
A’
A”
(4,-6)
(-4,6)
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Refresh Your Memory: Horizontal and Vertical Lines
Graph the following lines:– Y=5– Y=-2– X=4– X=-6
y
x
10
10
-10
-10
Y=5
Y=-2
X=4X=-6
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Graphing Coordinates
Plot the point A(4,6).
Reflect the point (4,6) over the line x=-1. Label this point A’.
Reflect the point (4,6) over the line y=2. Label this point A”.
y
x
10
10
-10
-10
AA’
A”(-6,6)
x=-1
y=2
(4,-2)
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More Reflection Examples
Graph the vertices of parallelogram WXYZ.– W(-3,5)– X(1,5)– Y(2,3)– Z(-2,3)
Reflect the parallelogram over the x-axis.
y
x
10
10
-10
-10
W X
YZ
W’X’
Y’Z’
W’(-3,-5)X’(1,-5)Y’(2,-3)Z’(-2,-3)
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More Reflection Examples
Graph the vertices of parallelogram WXYZ.– W(-3,1)– X(1,1)– Y(2,-1)– Z(-2,-1)
Reflect the parallelogram over the line x=-2
y
x
10
10
-10
-10
W X
YZx=-2
W’X’
Y’ Z’
W’(-1,1)X’(-5,1)Y’(-6,-1)Z’(-2,-1)
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Video Example
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Practice with Line Reflections
http://www.regentsprep.org/Regents/math/geometry/GT1/Prac1.htm
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More Practice:
The image of the point (4,-3) under a reflection across the x-axis is…
(4,3)
The image of the point (-5,4) under a reflection across the y-axis is…
(5,4)
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Think about it:
The image of the point (-1, 8) under a reflection across the line y = x is …
(8, -1)