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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
21/04/23 Reflections 13
Example 1
Reflection on Y-axis
Reflecting shapes
Reflect this shape
21/04/23 Reflections 17
1. Reflect this triangle in the y-axis
Reflect the shape in a mirror line
21/04/23 Reflections 18
1. Reflect this triangle in the y-axis
2. Draw lines from each vertex (corner) at 900 to the mirror line (y-axis)
21/04/23 Reflections 19
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
21/04/23 Reflections 20
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
21/04/23 Reflections 21
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
