Reflections in the Coordinate Plane
Reflecting over the x-axis: (the x-axis as the line of reflection)
When you reflect a point across the x-axis, the x-coordinate remains the same,
but the y-coordinate is transformed into its opposite.
The reflection of the point (x, y) across the x-axis is the point (x, -y).
or
Hint: If you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this
example the x-axis) to see where your new figure will be located. Or you can measure how far your points are away from the line
of reflection to locate your new image. Such processes will allow you to see what is happening to the coordinates and help you
remember the rule.
Reflecting over the y-axis: (the y-axis as the line of reflection)
When you reflect a point across the y-axis, the y-coordinate remains the same,
but the x-coordinate is transformed into its opposite.
The reflection of the point (x, y) across the y-axis is the point (-x, y).
or
Hint: If you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this
example the x-axis) to see where your new figure will be located. Or you can measure how far your points are away from the line
of reflection to locate your new image. Such processes will allow you to see what is happening to the coordinates and help you
remember the rule.
Geometry Common Core
Name: ____________________________________
Mr. Villegas
Date: ______________________________________
CLASS ACTIVITY
Reflecting over the x-axis: (the x-axis as the line of reflection)
a)
State the coordinates of every vertice from pre image( A, B, and C).
b) State the coordinates of every vertice from image ( A’, B’, and C’).
c)
Record your findings.
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d) Try to develop a plan or rule to help you remember the outcome of a refection in the x-axis.
Reflecting over the y-axis: (the y-axis as the line of reflection)
a)
State the coordinates of every vertice from pre image( A, B, and C).
b) State the coordinates of every vertice from image ( A’, B’, and C’).
c) Record your findings.
_________________________________________________________________________________________________
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_________________________________________________________________________________________________
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d) Try to develop a plan or rule to help you remember the outcome of a refection in the y-axis.
Lets put your plan or rule in action.
1) Point A is located at
1)
2)
3)
4)
2) When the point
1)
2)
3)
4)
. The point is reflected in the x-axis. Its image is located at
is reflected in the x-axis, what are the coordinates of its image?
3) What is the image of point
1)
2)
3)
4)
4) What are the coordinates of point
1)
2)
3)
4)
5) Point
1) I
2) II
3) III
4) IV
after a reflection in the x-axis?
after it is reflected over the x-axis?
is reflected in the x-axis. In which quadrant does its image lie?
6) Reflecting
in the y-axis yields an image of
1)
2)
3)
4)
Does your plan or rule work? Justify your answer.
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