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Unit 1B Review Problems.notebook
1
September 09, 2018
Unit 1B Review Problems.notebook
2
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
3
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: 180 degree clockwise OR counter clockwise rotation
Unit 1B Review Problems.notebook
4
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
5
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: reflection across the xaxis
Unit 1B Review Problems.notebook
6
September 09, 2018
What transformation took place to move A onto B? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
7
September 09, 2018
What transformation took place to move A onto B? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: translation (x + 7, y 3)
Unit 1B Review Problems.notebook
8
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
9
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: rotation of 90 degrees clockwise
Unit 1B Review Problems.notebook
10
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
11
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: 90 degree clockwise rotation
Unit 1B Review Problems.notebook
12
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
13
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: translation of (x 5, y + 3)
Unit 1B Review Problems.notebook
14
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
15
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: reflection across the xaxis
Unit 1B Review Problems.notebook
16
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
17
September 09, 2018
What transformation took place? Be specific.
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: reflection across the yaxis
Unit 1B Review Problems.notebook
18
September 09, 2018
A
B
C
Let's practice a reflection across the xaxis.
Unit 1B Review Problems.notebook
19
September 09, 2018
A
B
C
Let's practice a reflection across the xaxis.
A (6, 3) B (4, 0) C (1, 1)
A' (6, 3) B' (4, 0) C' (1, 1)
Unit 1B Review Problems.notebook
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September 09, 2018
A
B
C
Let's practice a reflection across the yaxis.
Unit 1B Review Problems.notebook
21
September 09, 2018
A
B
C
Let's practice a reflection across the yaxis. A (6, 3) B (4, 0) C (1, 1)
A' (6, 3) B' (4, 0) C' (1, 1)
Unit 1B Review Problems.notebook
22
September 09, 2018
A
B
C
Let's practice a translation of (x + 5, y 1).
Unit 1B Review Problems.notebook
23
September 09, 2018
A
B
C
Let's practice a translation of (x + 5, y 1)
A (6, 3) B (4, 0) C (1, 1)
A' (1, 4) B' (1, 1) C' (4, 2)
Unit 1B Review Problems.notebook
24
September 09, 2018
A
B
C
Let's practice a rotation of 180 degrees clockwise.
Unit 1B Review Problems.notebook
25
September 09, 2018
A
B
C
Let's practice a rotation of 180 degrees clockwise.* In 180 degree rotations, all of the coordinates stay in the same spot, but they change to their opposites.
A (6, 3) B (4, 0) C (1, 1)
A' (6, 3) B' (4, 0) C' (1, 1)
Unit 1B Review Problems.notebook
26
September 09, 2018
A
B
C
Let's practice a rotation of 90 degrees counterclockwise.
Unit 1B Review Problems.notebook
27
September 09, 2018
A
B
C
Let's practice a rotation of 90 degrees counterclockwise.In 90 degree rotations, you see which coordinate (the x or the y) "jumps over the top" and changes to its opposite.
A (6, 3) B (4, 0) C (1, 1)
A' (3, 6) B' (0, 4) C' (1, 1)
Unit 1B Review Problems.notebook
28
September 09, 2018
MULTIPLE TRANSFORMATIONSWhat transformations took
place? Be specific.• For translations, state how
much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
29
September 09, 2018
MULTIPLE TRANSFORMATIONSWhat transformations took
place? Be specific.• For translations, state how
much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: rotate 90 degrees counter clockwise (I drew the triangle in red after the rotation so I could see what I have to do next & you should do the same thing), then translate (x + 2, y + 0)
Unit 1B Review Problems.notebook
30
September 09, 2018
A
B
C
Z
Y
X
MULTIPLE TRANSFORMATIONSWhat transformations took place to map triangle ABC
onto triangle XYZ? Be specific.∆ABC ≅ ∆XYZ
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
31
September 09, 2018
A
B
C
Z
Y
X
MULTIPLE TRANSFORMATIONSWhat transformations took
place? Be specific.∆ABC ≅ ∆XYZ
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: Reflect across xaxis, thenTranslate (x + 0, y 4) (0 left/right & 4 down)
Unit 1B Review Problems.notebook
32
September 09, 2018
MULTIPLE TRANSFORMATIONSWhat transformations took
place to map triangle JMS onto triangle WDP ? Be specific.
∆JMS ≅ ∆WDP• For translations, state how
much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
Unit 1B Review Problems.notebook
33
September 09, 2018
MULTIPLE TRANSFORMATIONSWhat transformations took
place? Be specific.∆JMS ≅ ∆WDP
• For translations, state how much left/right and up/down
• For reflections, state over xaxis or yaxis
• For rotations, state how many degrees and in what direction
SOLUTION: Rotate 90 degrees clockwise & translate (x + 2, y + 0)
Unit 1B Review Problems.notebook
34
September 09, 2018
What angle is congruent to ∠Z?
What angle is congruent to ∠T?
What side is congruent to XY?
What side is the same length as SR?
Unit 1B Review Problems.notebook
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September 09, 2018
What angle is congruent to ∠Z?
What angle is congruent to ∠T?
What side is congruent to XY?
What side is the same length as SR?
Angle S
Angle X
TR
ZY
Unit 1B Review Problems.notebook
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September 09, 2018
What scale factor was used in the dilation?
Unit 1B Review Problems.notebook
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September 09, 2018
SOLUTION: You have two different options for solving these type of problems.
(1) Pick a vertex and its corresponding vertex.A (6, 6) A' (2, 2)
This is a reduction, so my scale factor has to be less than one, so I multiply 6 by 1/3 to get 2. My scale factor is 1/3.
OR (2) Use the "DO" ratio and onepair of corresponding angles.A (6, 6)= original; A' (2, 2) = dilatedDilated 2 1Original = 6 = 3* You can pick either the x valuesor the yvalues...you'll get the same solution either way!
Unit 1B Review Problems.notebook
38
September 09, 2018
Dilate the triangle by a scale factor of 1/3.
E
F
G
Unit 1B Review Problems.notebook
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September 09, 2018
Dilate the triangle by a scale factor of 1/3.
E
F
G
First you have to get your original ordered pairs.
E (3, 9) F (6, 0) G (12, 6) x x x x x x 1/3 1/3 1/3 1/3 1/3 1/3* Remember multiplying by 1/3 is the same as dividing by 3
E' (1, 3) F' (2, 0) G' (4, 2)
Make sure your answer is logical. My scale factor is 1/3, so the triangle should be reduced, and it was. Also, it should like EXACTLY like the original except for the size. it should NOT be rotated in any way.
Unit 1B Review Problems.notebook
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September 09, 2018
What scale factor was used in the dilation?
Unit 1B Review Problems.notebook
41
September 09, 2018
What scale factor was used in the dilation?
A (1, 3) A' (2, 6)
Dilated 2Original = 1 = 2
* Logical because it was enlarged, so scale factor has to be greater than 1!
Unit 1B Review Problems.notebook
42
September 09, 2018
What scale factor was used in the dilation?
Unit 1B Review Problems.notebook
43
September 09, 2018
What scale factor was used in the dilation?
A (2, 6) A' (1, 3)
Dilated 1Original = 2
* Logical because it was reduced, so scale factor has to be less than 1!
Unit 1B Review Problems.notebook
44
September 09, 2018
What scale factor was used in the dilation?
Unit 1B Review Problems.notebook
45
September 09, 2018
What scale factor was used in the dilation?
A (2, 2) A' (4, 4)
Dilated 4Original = 2 = 2
* Logical because it was enlarged, so scale factor has to be greater than 1!
Unit 1B Review Problems.notebook
46
September 09, 2018
What scale factor was used in the dilation?
Unit 1B Review Problems.notebook
47
September 09, 2018
What scale factor was used in the dilation?
A (2, 1) A' (6, 3)
Dilated 6Original = 2 = 3
* Logical because it was enlarged, so scale factor has to be greater than 1!
Unit 1B Review Problems.notebook
48
September 09, 2018
An actual airplane is 48 yards long and and 30 yards wide. A model airplane hanging from the ceiling in a museum is 8 yards long and 5 yards wide. What scale factor was used to create the model airplane?
Unit 1B Review Problems.notebook
49
September 09, 2018
An actual airplane is 48 yards long and and 30 yards wide. A model airplane hanging from the ceiling in a museum is 8 yards long and 5 yards wide. What scale factor was used to create the model airplane?
SOLUTION: Use the "DO" ratio to solve
48 yards corresponds to 8 yards because they are both length30 yards corresponds to 5 because they are both width, so choose either pair of corresponding sides, you don't use both.
Dilated 8 ÷ 8 = 1Original = 48 ÷ 8 = 6 * Logical because the model is a reduction of the actual *simplify the fraction airplane, so scale factor has to be less than 1!
Unit 1B Review Problems.notebook
50
September 09, 2018
Is triangle LMN similar to triangle GJF?
Unit 1B Review Problems.notebook
51
September 09, 2018
Is triangle LMN similar to triangle GJF?
SOLUTION: Set up a proportion with corresponding sides and see if your crossproducts are equal (similar) or not equal (not similar).
* Pick any TWO pairs of sides, you do NOT need all three sides.
LM MNGJ = JF
14 2721 = 42 NOT SIMILAR
588 567
Unit 1B Review Problems.notebook
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September 09, 2018
The two triangles are similar.What is the value of x?
Unit 1B Review Problems.notebook
53
September 09, 2018
The two triangles are similar.What is the value of x?
SOLUTION: choose two pair of corresponding sides to set up a proportion, then crossmultiply and divide. Remember, I need to see your crossproducts and what you are dividing by to earn full credit.
x 418 = 12
12x = 18 x 412x = 7212 12x = 6
Unit 1B Review Problems.notebook
54
September 09, 2018
The two triangles are similar.What is the value of x?
Unit 1B Review Problems.notebook
55
September 09, 2018
The two triangles are similar.What is the value of x?
SOLUTION: choose two pair of corresponding sides to set up a proportion, then crossmultiply and divide. Remember, I need to see your crossproducts and what you are dividing by to earn full credit.
x 12 2 = 4
4x = 12 x 24x = 244 4x = 6
Unit 1B Review Problems.notebook
56
September 09, 2018
The two triangles are similar.What is the value of x?
Unit 1B Review Problems.notebook
57
September 09, 2018
The two triangles are similar.What is the value of x?
SOLUTION: choose two pair of corresponding sides to set up a proportion, then crossmultiply and divide. Remember, I need to see your crossproducts and what you are dividing by to earn full credit.
x 38 * You have to add 16 + 22 to get the entire bottom side
17 = 16
16x = 17 x 3816x = 64616 16x = 40.375
Unit 1B Review Problems.notebook
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September 09, 2018
This is a picture of the world's tallest man and the world's shortest man. The tallest man casts a 73.5 inch shadow. At the same time of day, the shortest man, who stands 24 inch tall, casts an 18 inch long shadow. How tall is the world's tallest man?
Unit 1B Review Problems.notebook
59
September 09, 2018
This is a picture of the world's tallest man and the world's shortest man. The tallest man casts a 73.5 inch shadow. At the same time of day, the shortest man, who stands 24 inch tall, casts an 18 inch long shadow. How tall is the world's tallest man? Draw a picture to see the corresponding sides!
24
18x
73.5 x 73.524 = 18
18x = 73.5 x 2418x = 176418 18x = 98 inches
