Geometric Transformation. A reflection of an object is the 'flip' of that object over a line, called the line of reflection. Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.

1. reflection

2. Reflection
An object can be reflected in a mirror line or axis of
reflection to produce an image of the object.
For example,
Each point in the image must be the same distance from
the mirror line as the corresponding point of the original
object.

3. Reflecting shapes
If we reflect the quadrilateral ABCD in a mirror line we label
the image quadrilateral A’B’C’D’.
A
B
C
D
A’
B’
C’
D’
pre-image reflection
mirror line or axis of reflection
The image is congruent to the original shape.

4. A
B
C
D
A’
B’
C’
D’
object image
mirror line or axis of reflection
Reflecting shapes
If we draw a line from any point on the object to its image
the line forms a perpendicular bisector to the mirror line.

5. Reflecting shapes

6. Reflecting shapes by folding paper
We can make reflections by folding paper.
Draw a random polygon at the top of a piece of
paper.
Fold the piece of paper back on itself so you
can still see the shape.
Pierce through each vertex of the shape using a compass
point.
When the paper is unfolded the vertices of the
image will be visible.
Join the vertices together using a ruler.

7. Reflecting shapes using tracing paper
Suppose we want to reflect this
shape in the given mirror line.
Use a piece of tracing paper to
carefully trace over the shape and
the mirror line with a soft pencil.
When you turn the tracing paper
over you will see the following:
Place the tracing paper over the
original image making sure the
symmetry lines coincide.
Draw around the outline on the back of the tracing paper
to trace the image onto the original piece of paper.

8. Reflect this shape

9. Reflection on a coordinate grid
The vertices of a
triangle lie on the
points A(2, 6), B(7, 3)
and C(4, –1).
0 1 2 3 4 5 6 7–1–2–3–4–5–6–7
1
2
3
4
5
6
7
–2
–4
–6
–3
–5
–7
–1
A(2, 6)
B(7, 3)
C(4, –1)
Reflect the triangle in
the y-axis and label
each point on the
image.
A’(–2, 6)
B’(–7, 3)
C’(–4, –1)
What do you notice
about each point
and its image?
x
y

10. Reflection on a coordinate grid
The vertices of a
quadrilateral lie on
the points A(–4, 6),
B(4, 5), C(2, –2) and
D(–5, 3).
0 1 2 3 4 5 6 7–1–2–3–4–5–6–7
1
2
3
4
5
6
7
–2
–4
–6
–3
–5
–7
–1
A(–4, 6)
B(4, 5)
C(2, 0)
Reflect the quadrilateral
in the x-axis and label
each point on the image.
A’(–4, –6)
B’(4, –5)
D’(–5, –3)
What do you notice
about each point
and its image?
D(–5, 3)
C’(2, 0)
x
y

11. Reflection on a coordinate grid
The vertices of a
triangle lie on the
points A(4, 4), B(7, –1)
and C(2, –6).
0 1 2 3 4 5 6 7–1–2–3–4–5–6–7
1
2
3
4
5
6
7
–2
–4
–6
–3
–5
–7
–1
A(4, 4)
C(2, –6)
Reflect the triangle in
the line y = x and
label each point on
the image.
A’(4, 4)
B’(–1, 7)
C’(–6, 2)
x = y
What do you notice
about each point
and its image?
x
y
B(7, –1)