Transformations Reflection An object can be reflected in a mirror line or axis of reflection to...

Transformations

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.

ReflectionAn 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.

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.The image is congruent to the original shape.

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.

Reflecting shapes

Reflecting shapes

Reflect this shape

Finding a line of reflectionConstruct the line that reflects shape A onto its image A’.

A’

A This is the line of reflection.

Draw lines from any two vertices to their images.

Draw a line through the mid points.

Mark on the mid-point of each line.

Reflection on X-axis

Reflect this shape

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Example 1

Reflection on Y-axis

Reflecting shapes

Reflect this shape

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1. Reflect this triangle in the y-axis

Reflect the shape in a mirror line

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1. Reflect this triangle in the y-axis

2. Draw lines from each vertex (corner) at 900 to the mirror line (y-axis)

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1. Reflect this triangle in the y-axis

2. Draw lines from each vertex (corner) at 900 to the mirror line (y-axis)

3. Use these lines to find the reflected points

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1. Reflect this triangle in the y-axis

2. Draw lines from each vertex (corner) at 900 to the mirror line (y-axis)

3. Use these lines to find the reflected points

4. Draw the reflection

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Example

Reflection on the line Y =X

Reflect this shape

Reflection on the line Y = -X

Reflect this shape

Reflection on the line x = h

Reflect this shape

Reflection on the line y = k

Reflect this shape

Reflection Summary

• Reflection on X-axis: P(x, y) P’(x, -y)• Reflection on Y-axis: P(x, y) P’(-x, y)• Reflection on y= x: P(x, y) P’(y, x)• Reflection on y = - x: P(x, y) P’(-y, -x)• Reflection on x = h: P(x, y) P’(2h-x, y)• Reflection on y = k: P(x, y) P’(x, 2k-y)

Note: X-axis means y = 0Y-axis means x = 0Line parallel to X-axis means y = kLine parallel to Y-axis means x = h

Reflect this shape

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

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

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)

Reflect this shape

Reflection on a coordinate grid

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

e.g.

Reflect the object shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

Turn tracing paper over and match up mirror lines/square corners.

Mirror Line

object

image

Mark position of vertices, remove tracing paper and draw image of shape.

Reflections Using Tracing Paper

Tracing 1

Reflections Using Tracing Paper

object

Mirror Line

Reflect the object shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

Turn tracing paper over and match up mirror lines.

object

Mirror Line

Reflect the shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

Turn tracing paper over and match up mirror lines.

Mark position of vertices, remove tracing paper and draw image of shape.

Reflections Using Tracing Paper

Mirror Line

Reflect the shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

Turn tracing paper over and match up mirror lines.

Mark position of vertices, remove tracing paper and draw image of shape.

object image

Reflections Using Tracing Paper

Tracing 2Mirror Line

Reflect the object shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

object

Turn tracing paper over and match up mirror lines.

Reflections Using Tracing Paper

Mirror Line

Reflect the object shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

object

Turn tracing paper over and match up mirror lines.

Mark position of vertices, remove tracing paper and draw image of shape.

Reflections Using Tracing Paper

Mirror Line

Reflect the object shape in the mirror line shown.

Trace the shape and mirror line using tracing paper.

object

Turn tracing paper over and match up mirror lines.

Mark position of vertices, remove tracing paper and draw image of shape.

image

Reflections Using Tracing Paper