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© Boardworks Ltd 20151 of 9
G13 Reflection and symmetry
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Reflection
An object can be reflected in a mirror line or axis of reflection to produce an image of the object.
Each point in the image must be the same distance from the mirror line as the corresponding point of the original object.
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Reflecting shapes
If we reflect the quadrilateral ABCD in a mirror line we label the image quadrilateral A’B’C’D’.
A
B
CD
A’
B’
C’D’
object image
mirror line or axis of reflection
The image is congruent to the original shape.
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A
B
CD
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.
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Reflecting shapes
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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
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Reflection symmetry
If you can draw a line through a shape so that one half is a reflection of the other then the shape has reflection or line symmetry.
The mirror line is called a line of symmetry.
one line of symmetry
two lines of symmetry
no lines of symmetry
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Reflection symmetry
How many lines of symmetry do the following designs have?
one line of symmetry
five lines of symmetry
three lines of symmetry
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Make this shape symmetrical
