Graphing and Describing Dilationsimages.pcmac.org/SiSFiles/Schools/MS/DeSotoCounty/...Graphing and Describing Dilations 3 | P a g e Describing a Dilation When being asked to describe

Graphing and Describing Dilations

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Teacher Lesson Plan Lesson: Day 7 – 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 TSW… Graph dilations. TSW… 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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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 ¼ . dilation with a scale factor of 2. Pre-Image Pre-Image Coordinates Coordinates

Image Image

Coordinates Coordinates

Student Notes

𝐉(𝟑, 𝟖)

𝐊(𝟏𝟎, 𝟔)

𝐋(𝟖, 𝟐)

Pre-Image

A figure has vertices:

Graph the figure and the image of the figure after a dilation with a scale factor of ½.

𝐉’ ( , )

𝐊’ ( , )

𝐋’ ( , )

Image

𝐅(−𝟏, 𝟏)

𝐆(𝟏, 𝟏)

𝐇(𝟐, − 𝟏)

𝐈(−𝟏, − 𝟏)

Pre-Image


Graph the figure and the image of the figure after a dilation with a scale factor of 4.

𝐅’ ( , )

𝐆’ ( , )

𝐇’ ( , )

𝐈′ ( , )

Image


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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 “2” to create the image W’X’Y’Z’

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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Name________________________________ Date______________ Period_____

Dilations

Directions: Perform each dilation and write the coordinates as specified. 1) 2)

Classwork


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3)

4) The table below shows the coordinates of triangle RST and the coordinates of R’ in triangle R’S’T’. Triangle R’S’T’ is a dilation of triangle RST.

Part A What are the coordinates of point S’ and point T’? Part B On the grid below, draw triangle RST and triangle R’S’T’.


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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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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 ¼ . 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 P’ (0, -1) Q’ (2, -1) W’ (6, 8) X’(10, 8) R’ (2, -2) S’ (0, -2) Y’ (-4, -6) Z’(-8, -6)

Student Notes

𝐉(𝟑, 𝟖)

𝐊(𝟏𝟎, 𝟔)

𝐋(𝟖, 𝟐)

Pre-Image


Graph the figure and the image of the figure after a dilation with a scale factor of ½.

𝐉’ (𝟏𝟏

𝟐, 𝟒)

𝐊’ (𝟓, 𝟑)

𝐋’ (𝟒, 𝟏)

Image

𝐅(−𝟏, 𝟏)

𝐆(𝟏, 𝟏)

𝐇(𝟐, − 𝟏)

𝐈(−𝟏, − 𝟏)

Pre-Image


Graph the figure and the image of the figure after a dilation with a scale factor of 4.

𝐅’ (−𝟒, 𝟒)

𝐆’ (𝟒, 𝟒)

𝐇’ (𝟖, −𝟒)

𝐈′ (−𝟒, −𝟒)

Image

Answer Key


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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 “2” to create the image W’X’Y’Z’

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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Name________________________________ Date______________ Period_____

Dilations

Directions: Perform each dilation and write the coordinates as specified. 1) 2)

Classwork


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3)

4) The table below shows the coordinates of triangle RST and the coordinates of R’ in triangle R’S’T’. Triangle R’S’T’ is a dilation of triangle RST.

Part A What are the coordinates of point S’ and point T’? 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 R’S’T’.


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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

Documents

Graphing and Describing Dilationsimages.pcmac.org/SiSFiles/Schools/MS/DeSotoCounty/...Graphing and Describing Dilations 3 | P a g e Describing a Dilation When being asked to describe