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G13 Reflection and symmetry
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G13.1 Reflection
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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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Reflecting shapes by folding paper
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Reflecting shapes using tracing paper
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Reflect this shape
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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 on a coordinate grid
The vertices of a quadrilateral lie on the points A(–4, 6), B(4, 5), C(2, 0) 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
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–7
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
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)
