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Graphing and Describing Dilations
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Teacher Lesson Plan Lesson: Day 7 β Supplement Lesson Graphing and Describing Dilations CC Standards 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Objective TSWβ¦ Graph dilations. TSWβ¦ Describe what happens to the coordinates when dilation is performed. Mathematical Practices #1 Make sense of problems and persevere in solving them. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning. Note to teachers:
Be sure to teach this lesson from the PowerPoint, not the student notes. You will be missing most of the lesson otherwise. Teacher Input Bellwork: Review bellwork. Homework: Review important problems assigned the previous night. Introduction: Introduce as directed on the PowerPoint. Lesson: Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional
instruction and answers. Practice Classwork Pages 4-5 Homework Pages 6 Closure See closure slide on PowerPoint.
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Graphing and Describing Dilations
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Steps for graphing a Dilation
Step 1: Graph and determine the coordinates of the original shape as needed. Step 2: Multiply the coordinates of each vertex by the scale factor. (x, y) --> (kx, ky) where k is the scale factor Step 3: Graph the vertices of the new image and label them with prime symbols.
Guided Practice #1
Guided Practice #2
You Try #1 You Try #2
Graph the image of the figure after a Graph the image of the figure after a dilation with a scale factor of ΒΌ . dilation with a scale factor of 2. Pre-Image Pre-Image Coordinates Coordinates
Image Image
Coordinates Coordinates
Student Notes
π(π, π)
π(ππ, π)
π(π, π)
Pre-Image
A figure has vertices:
Graph the figure and the image of the figure after a dilation with a scale factor of Β½.
πβ ( , )
πβ ( , )
πβ ( , )
Image
π (βπ, π)
π(π, π)
π(π, β π)
π(βπ, β π)
Pre-Image
A figure has vertices:
Graph the figure and the image of the figure after a dilation with a scale factor of 4.
π β ( , )
πβ ( , )
πβ ( , )
πβ² ( , )
Image
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Graphing and Describing Dilations
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Describing a Dilation
When being asked to describe a dilation that has taken place, you are usually being asked to identify a scale factor. Was the shape reduced or enlarged and by how much.
If you are given two shapes and need to find the scale factor, you must know which one was the original and which one is the new image. Then you need to know the length of corresponding sides and set them up in a ratio like so:
Example: Describe the dilation that was performed below.
Figure WXYZ was enlarged by a scale factor of β2β to create the image WβXβYβZβ
Directions: On each graph, one figure is a dilation of the other. Find the scale factor of each dilation and classify it as an enlargement or as a reduction.
Guided Practice
You Try
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Graphing and Describing Dilations
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Name________________________________ Date______________ Period_____
Dilations
Directions: Perform each dilation and write the coordinates as specified. 1) 2)
Classwork
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Graphing and Describing Dilations
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3)
4) The table below shows the coordinates of triangle RST and the coordinates of Rβ in triangle RβSβTβ. Triangle RβSβTβ is a dilation of triangle RST.
Part A What are the coordinates of point Sβ and point Tβ? Part B On the grid below, draw triangle RST and triangle RβSβTβ.
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Graphing and Describing Dilations
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Name________________________________ Date______________ Period_____ Translations, Reflections, Rotations, Dilations
Directions: Perform each transformation. Label using prime notation.
1) 2)
3) 4)
5) 6)
Homework
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Graphing and Describing Dilations
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Graphing and Describing Dilations
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Steps for graphing a Dilation
Step 1: Graph and determine the coordinates of the original shape as needed. Step 2: Multiply the coordinates of each vertex by the scale factor. (x, y) --> (kx, ky) where k is the scale factor Step 3: Graph the vertices of the new image and label them with prime symbols.
Guided Practice #1
Guided Practice #2
You Try #1 You Try #2
Graph the image of the figure after a Graph the image of the figure after a dilation with a scale factor of ΒΌ . dilation with a scale factor of 2. Pre-Image Pre-Image Coordinates Coordinates P (0, -4) Q (8, -4) W (3, 4) X (5, 4) R (8, -8) S (0, -8) Y (-2, -3) Z (-4, -3)
Image Image
Coordinates Coordinates Pβ (0, -1) Qβ (2, -1) Wβ (6, 8) Xβ(10, 8) Rβ (2, -2) Sβ (0, -2) Yβ (-4, -6) Zβ(-8, -6)
Student Notes
π(π, π)
π(ππ, π)
π(π, π)
Pre-Image
A figure has vertices:
Graph the figure and the image of the figure after a dilation with a scale factor of Β½.
πβ (ππ
π, π)
πβ (π, π)
πβ (π, π)
Image
π (βπ, π)
π(π, π)
π(π, β π)
π(βπ, β π)
Pre-Image
A figure has vertices:
Graph the figure and the image of the figure after a dilation with a scale factor of 4.
π β (βπ, π)
πβ (π, π)
πβ (π, βπ)
πβ² (βπ, βπ)
Image
Answer Key
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Graphing and Describing Dilations
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Describing a Dilation
When being asked to describe a dilation that has taken place, you are usually being asked to identify a scale factor. Was the shape reduced or enlarged and by how much.
If you are given two shapes and need to find the scale factor, you must know which one was the original and which one is the new image. Then you need to know the length of corresponding sides and set them up in a ratio like so:
Example: Describe the dilation that was performed below.
Figure WXYZ was enlarged by a scale factor of β2β to create the image WβXβYβZβ
Directions: On each graph, one figure is a dilation of the other. Find the scale factor of each dilation and classify it as an enlargement or as a reduction.
Guided Practice
Enlargement; Scale Factor = 3/2 or 1.5 Enlargement; Scale Factor = 2 Reduction; Scale Factor = 2/5
You Try
Enlargement; Scale Factor = 2 Reduction; Scale Factor = 2/3
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Graphing and Describing Dilations
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Name________________________________ Date______________ Period_____
Dilations
Directions: Perform each dilation and write the coordinates as specified. 1) 2)
Classwork
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Graphing and Describing Dilations
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3)
4) The table below shows the coordinates of triangle RST and the coordinates of Rβ in triangle RβSβTβ. Triangle RβSβTβ is a dilation of triangle RST.
Part A What are the coordinates of point Sβ and point Tβ? Use either the x or y coordinate to find the scale factor. New Image -6 Scale Factor = 3 Original -2
Part B On the grid below, draw triangle RST and triangle RβSβTβ.
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Graphing and Describing Dilations
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Name________________________________ Date______________ Period_____ Translations, Reflections, Rotations, Dilations
Directions: Perform each transformation. Label using prime notation.
1) 2) 3) 4)
5) 6)
Homework