2. Goals
By the end of this lesson, you should be
able to:
ā¦ Reļ¬ect images over parallel lines
ā¦ Deļ¬ne composite, composition,
translation. You should also be able to
determine the magnitude and direction of
a translation.
ā¦ Demonstrate the use of the three steps
needed from the Two Reļ¬ections Theorem
For Translations.
3. Creating a Reļ¬ection of
a Reļ¬ection
If you have t wo parallel lines and you
need to ļ¬nd the point of the reļ¬ection.
7. Properties of
Translations
A translation is fully described only
when itās magnitude and direction are
known.
8. Point of Reļ¬ection
If you have t wo parallel lines and you need to ļ¬nd the
point of reļ¬ection...
9. Point of Reļ¬ection
If you have t wo parallel lines and you need to ļ¬nd the
point of reļ¬ection...
rm (I) The I is your starting point
Identify the point by a
single letter
rm (I)
10. Point of Reļ¬ection
If you have t wo parallel lines and you need to ļ¬nd the
point of reļ¬ection...
rm (I) The I is your starting point
Draw t wo lines
that connect
point I to line m.
Identify the point by a
single letter
rm (I)
11. Point of Reļ¬ection
If you have t wo parallel lines and you need to ļ¬nd the
point of reļ¬ection...
rm (I) The I is your starting point
Draw t wo lines
that connect
point I to line m.
Make one
reļ¬ection of the
image drawn
Identify the point by a
single letter
rm (I)
12. Point of Reļ¬ection
If you have t wo parallel lines and you need to ļ¬nd the
point of reļ¬ection...
rm (I) The I is your starting point
Draw t wo lines
that connect
point I to line m.
Make one
reļ¬ection of the
image drawn
Identify the point by a
single letter
rm (I) Your answer is C
13. Now you try...
Identify the point by a
single letter
rn(E)
16. Howād you do?
rn (E) The E is your starting point
Draw t wo lines
that connect
point E to line n.
17. Howād you do?
rn (E) The E is your starting point
Draw t wo lines
that connect
point E to line n.
Make one
reļ¬ection of the
image drawn
18. Howād you do?
rn (E) The E is your starting point
Draw t wo lines
that connect
point E to line n.
Make one
reļ¬ection of the
image drawn
Your answer is A
19. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1.
20. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1.
21. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your
starting point
rc rb (E)
Starting point
22. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
rc rb (E)
Starting point
23. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
2. If the line given ļ¬rst is +
on the right then put
t wo plus signs (if going +
to left put t wo minus
signs).
rc rb (E)
Starting point
ļ¬rst given line
24. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
distance=6
2. If the line given ļ¬rst is +
on the right then put
t wo plus signs (if going +
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rc rb (E) and write it t wice
Starting point
ļ¬rst given line
25. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
distance=6
2. If the line given ļ¬rst is + 6
on the right then put
t wo plus signs (if going +
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rc rb (E) and write it t wice
Starting point
ļ¬rst given line
26. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
distance=6
2. If the line given ļ¬rst is + 6
on the right then put
t wo plus signs (if going + 6
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rc rb (E) and write it t wice
Starting point
ļ¬rst given line
27. Learning the Two Reļ¬ections Theorem for
Translations with 3 steps
1. Find the value of your 1
starting point
distance=6
2. If the line given ļ¬rst is + 6
on the right then put
t wo plus signs (if going + 6
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rc rb (E) and write it t wice
Starting point 13
ļ¬rst given line
28. Now You Try...
Find the value of your
starting point
rb rc (D)
29. Howād You Do?
1. Find the value of your
starting point
distance=6
2. If the line given ļ¬rst is
on the right then put
t wo plus signs (if going
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
30. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is
on the right then put
t wo plus signs (if going
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
31. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is -
on the right then put
t wo plus signs (if going
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
32. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is -
on the right then put
t wo plus signs (if going -
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
33. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is - 6
on the right then put
t wo plus signs (if going -
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
34. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is - 6
on the right then put
t wo plus signs (if going - 6
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point
ļ¬rst given line
35. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is - 6
on the right then put
t wo plus signs (if going - 6
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point -14
ļ¬rst given line
36. Howād You Do?
1. Find the value of your -2
starting point
distance=6
2. If the line given ļ¬rst is - 6
on the right then put
t wo plus signs (if going - 6
to left put t wo minus
signs).
3. Find the distance
bet ween the t wo lines
rb rc (D) and write it t wice
Starting point Answer = -14
ļ¬rst given line