Dilations and Similarity

Lesson 8

Math

Unit 3

10th Grade

Lesson 8 of 18

Objective


Dilate a figure on the coordinate plane when the center of dilation is the origin.

Common Core Standards


Core Standards

  • G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • G.SRT.A.2 — Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Foundational Standards

  • 8.G.A.3

Criteria for Success


  1. Describe that a figure that is dilated is stretched proportionally and that this needs to be accounted for when the figure is on the coordinate plane through $${{x-}}$$ and $${{y-}}$$coordinates. 
  2. Describe how to dilate a figure on the coordinate plane with a center of the origin by multiplying the $${{x-}}$$ and $${{y-}}$$coordinates by the scale factor. 
  3. Use the notation for showing the dilation of $${(x,y)\rightarrow(rx,ry)}$$, where $$r$$ is the scale factor. 
  4. Verify the properties of dilations when the figure is dilated on the coordinate plane. 
  5. Compare the process for performing dilations on and off the coordinate plane.
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Anchor Problems

25-30 minutes


Problem 1

Sketch the dilation of the following figure by a scale factor of $$2$$ with a center of dilation of $$D$$. What is your process for dilating this figure?

Guiding Questions

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Problem 2

Use the graph below to answer the questions that follow:

 

  1. Multiply JUST the $${{x-}}$$coordinate by $$3$$. Plot the point and label the point $$A$$.

  2. Multiply JUST the $${{y-}}$$coordinate by $$3$$. Plot the point and label the point $$B$$.

  3. Multiply both the $${{x-}}$$ and $${{y-}}$$coordinate by $$3$$. Plot the point and label the point $$C$$.

Guiding Questions

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Problem 3

Dilate the following figure when the center of dilation is the origin and the scale factor is 1.5.

Guiding Questions

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Target Task

5-10 minutes


Scale the following figure by the rule shown when the center of dilation is the origin.

$${(x,y)\rightarrow\left ( \frac{2}{3}x,\frac{2}{3}y \right )}$$

Next

Dilate a figure when the center of dilation is not the origin. Determine center of dilation given the original and dilated figure.

Lesson 9
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Lesson Map

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Topic A: Dilations off the Coordinate Plane

Topic B: Dilations on the Coordinate Plane

Topic C: Defining Similarity

Topic D: Similarity Applications

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