View
217
Download
2
Category
Preview:
Citation preview
1 of 66
GCSE Maths Starter 31. What is 2/3 of 210?2. Solve the equation to find x: 4(x+5) = 443. What is the probability of throwing a 4 on an
ordinary dice?4. Draw a circle and label the radius and
diameter.5. Describe the correlation in the scatter graph.
x xx xx
xx
x
xxx
Price
of Ca
r Age of Car
2 of 66
Lesson 3 Reflections and Translations
Mathswatch Clip 75/77.
• To know the sort of movement a reflection and translation is. (Grade E)
• To reflect and translate objects correctly. (Grade D)
• To describe translations and reflections fully. (Grade D/C)
EXTN: To be able to describe reflections when the mirror line is given as an equation such as
y = x, or y = 2 etc. (Grade C)
3 of 66
Reflection symmetryIf you can draw a line through a shape so that one half is the mirror image of the other then the shape has reflection or line symmetry.
The mirror line is called a line of symmetry.
one line of symmetry
four lines of symmetry
no lines of symmetry
Lesson 3 Reflection and Translations.Mathswatch 75/77.
4 of 66
Reflection symmetryHow many lines of symmetry do the following designs have?
five lines of symmetry
three lines of symmetry
one line of symmetry
Lesson 3 Reflection and Translations.Mathswatch 75/77.
5 of 66
Reflection symmetry in 3-D shapes
We can divide the cube into two symmetrical parts here.
How many planes of symmetry does a cube have?
Lesson 3 Reflection and Translations.Mathswatch 75/77.
6 of 66
Reflection symmetry in 3-D shapesHow many planes of symmetry does a cuboid have?
A cuboid has three planes of symmetry.
Lesson 3 Reflection and Translations.Mathswatch 75/77.
7 of 66
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.
Lesson 3 Reflection and Translations.Mathswatch 75/77.
8 of 66
Reflecting shapesIf 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.
Lesson 3 Reflection and Translations.Mathswatch 75/77.
9 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
10 of 66
Reflection on a coordinate grid
Lesson 3 Reflection and Translations.Mathswatch 75/77.
11 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
Where would the line x = 4 be?
12 of 66
TranslationWhen an object is moved in a straight line in a given direction we say that it has been translated.
For example, we can translate triangle ABC 5 squares to the right and 2 squares up.
C
A
B
object
C
A
B
object
C
A
B
object
C
A
B
object
C
A
B
object
C
A
B
object
C
A
B
object
C
A
B
object C’
A’
B’
image
Every point in the shape moves the same distance in the same direction.
We can describe this translation using the vector .52
Lesson 3 Reflection and Translations.Mathswatch 75/77.
13 of 66
Describing translationsWhen we describe a translation we always give the movement left or right first followed by the movement up or down.
We can also describe translations using vectors.
As with coordinates, positive numbers indicate movements up or to the right and negative numbers are used for movements down or to the left.
For example, the vector describes a translation 3 right and 4 down.
3–4
Lesson 3 Reflection and Translations.Mathswatch 75/77.
14 of 66
Translations on a coordinate grid
15 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
16 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
17 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
18 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
19 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
20 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
21 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
22 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
This is a typical exam question.
What does the vector tell you to do to the shape?
Where would the translated shape go?
4 Right3 Down4 Right3 Down
23 of 66
Lesson 3 Reflection and Translations.Mathswatch 75/77.
Now it is your turn.
24 of 66
Lesson 3 Reflections and Translations
Mathswatch Clip 75/77.
• To know the sort of movement a reflection and translation is. (Grade E)
• To reflect and translate objects correctly. (Grade D)
• To describe translations and reflections fully. (Grade D/C)
EXTN: To be able to describe reflections when the mirror line is given as an equation such as
y = x, or y = 2 etc. (Grade C)
Recommended