9.1
Reflections
By: The Tortellini's
Draga, Kristin, Saahithi
Objectives
 Identifying
and drawing reflections.
 Reflections
in the coordinate plane.
Vocabulary
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Isometry: A transformation that does not
change the shape or size of a figure, also
known as congruence transformations or rigid
transformations.
Reflection: A transformation that moves a
figure by flipping it across a line.
Preimage: The figure before it is flipped over
the line.
Image: The figure once it is flipped or
reflected over the line.
Identifying Reflections
A
transformation is a reflection if it
appears to be flipped across a line.
Examples of Reflections
A. Not a reflection because
the image is not flipped
over a line.
B. This is a reflection.
because the image
is flipped over the line.
More on Reflections
A
reflection is a transformation across a
line, called the line of reflection, so that
line of reflection is the perpendicular
bisector of each segment joining each
point and its image.
Steps in drawing reflections
1.
2.
3.
4.
5.
Copy the quadrilateral and the line of reflection.
Draw the reflection of the quadrilateral across the line.
Through each line draw a line perpendicular to the line of
reflection.
Measure the distance from each vertex to the line of
reflection. Locate the image of each vertex on the opposite
side of the line of reflection and the same distance from it.
Connect the images of the vertices.
Word problem with a
reflection being drawn
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A trail designer is planning two trails that connect
campsites A and B to a point on the river. He wants the
total length of the trails to be as short as possible. Where
should the trail meet the river?
Reflections in the coordinate plane
Across the y-axis
Across the x-axis
Across the line y = x
Drawing reflections in the coordinate plane
Reflect the figure with the given vertices across the give
line.
Example #1
M(1,2),N(1,4),P(3,3):y-axis
The reflection of (x,y) is (-x,y).
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Drawing reflections in the coordinate plane
Example #2
D(2,0),E(2,2),F(5,2),G(5,1);y = x
The reflection of (x,y) is (y,x).
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