Transformations Reflection An object can be reflected in a mirror line or axis of reflection to...
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Transcript of Transformations Reflection An object can be reflected in a mirror line or axis of reflection to...
![Page 1: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/1.jpg)
Transformations
![Page 2: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/2.jpg)
![Page 3: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/3.jpg)
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.
![Page 4: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/4.jpg)
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.
![Page 5: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/5.jpg)
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.
![Page 6: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/6.jpg)
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.
![Page 7: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/7.jpg)
Reflecting shapes
![Page 8: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/8.jpg)
Reflecting shapes
![Page 9: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/9.jpg)
Reflect this shape
![Page 10: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/10.jpg)
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.
![Page 11: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/11.jpg)
Reflection on X-axis
![Page 12: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/12.jpg)
Reflect this shape
![Page 13: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/13.jpg)
21/04/23 Reflections 13
Example 1
![Page 14: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/14.jpg)
Reflection on Y-axis
![Page 15: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/15.jpg)
Reflecting shapes
![Page 16: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/16.jpg)
Reflect this shape
![Page 17: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/17.jpg)
21/04/23 Reflections 17
1. Reflect this triangle in the y-axis
Reflect the shape in a mirror line
![Page 18: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/18.jpg)
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)
![Page 19: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/19.jpg)
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
![Page 20: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/20.jpg)
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
![Page 21: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/21.jpg)
21/04/23 Reflections 21
Example
![Page 22: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/22.jpg)
Reflection on the line Y =X
![Page 23: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/23.jpg)
Reflect this shape
![Page 24: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/24.jpg)
Reflection on the line Y = -X
![Page 25: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/25.jpg)
Reflect this shape
![Page 26: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/26.jpg)
Reflection on the line x = h
![Page 27: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/27.jpg)
Reflect this shape
![Page 28: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/28.jpg)
Reflection on the line y = k
![Page 29: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/29.jpg)
Reflect this shape
![Page 30: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/30.jpg)
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
![Page 31: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/31.jpg)
Reflect this shape
![Page 32: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/32.jpg)
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
![Page 33: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/33.jpg)
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
![Page 34: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/34.jpg)
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)
![Page 35: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/35.jpg)
Reflect this shape
![Page 36: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/36.jpg)
Reflection on a coordinate grid
![Page 37: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/37.jpg)
What letter would you get if you reflected each shape in its corresponding mirror line?
![Page 38: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/38.jpg)
What letter would you get if you reflected each shape in its corresponding mirror line?
![Page 39: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/39.jpg)
What letter would you get if you reflected each shape in its corresponding mirror line?
![Page 40: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/40.jpg)
What letter would you get if you reflected each shape in its corresponding mirror line?
![Page 41: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/41.jpg)
What letter would you get if you reflected each shape in its corresponding mirror line?
![Page 42: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/42.jpg)
e.g.
![Page 43: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/43.jpg)
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
![Page 44: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/44.jpg)
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.
![Page 45: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/45.jpg)
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
![Page 46: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/46.jpg)
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
![Page 47: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/47.jpg)
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
![Page 48: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/48.jpg)
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
![Page 49: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062322/5697bf7b1a28abf838c833c7/html5/thumbnails/49.jpg)
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