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Understanding Dilations and Scale Factors in Geometry

In this lesson, students will explore the concept of dilations, a transformation that alters the size of a geometric figure without changing its shape. They will rewrite definitions related to dilations, such as isometry and scale factor, in their own words and illustrate these concepts through sketches. The session will focus on how coordinates can be utilized to resize figures and the differences between dilations and congruence. Additionally, students will engage in formative assessments and complete a homework worksheet to reinforce their understanding.

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Understanding Dilations and Scale Factors in Geometry

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  1. Unit 1 – Day 4 Dilations

  2. Warm Up #2 (1.28.2014) Individually, rewrite your definitions WITHOUT using the vocabulary term. Then sketch a picture of 2-4. • Isometry • Translation • Reflection • Rotation e.g. Rotation is not “rotating an object”

  3. Essential Question1.28.2014 How can coordinates be used to rescale or resize a shape?

  4. Dilation • Definition: A Dilation is a transformation that resizes a figure. • It can get bigger or smallerbut is still the same shape. • Does a dilation have the property of isometry? • NO!!! Dilations create similar figures, not congruent figures!

  5. All Dilations have a scale factor Definition: A Scale Factoris how much a figure changes in size

  6. http://www.mathopenref.com/dilate.html

  7. How do you go from A to A’ Does that work for • B to B’? • C to C’?

  8. General Rule for Dilation Dilation by scale factor c (x, y)  (cx, cy) or (x, y)c(x, y)

  9. If given a preimage and an image how do you find the scale factor? A’ or A need to be either the x’s or the y’s of one coordinate, Unless the values are zero.

  10. Ex. Find the scale factor The preimage of Triangle ABC has coordinates A(24, 4), B(4, 6), and C(12, 8). The image of Triangle A’B’C’ has coordinates A’(6, 1), B’(1, 1.5), and C’(3, 2). a) What is scale factor? b) Write a rule to describe this transformation.

  11. Assessment • 3-2-1: Write down 3 things you learned today, 2 things you have a question about, and 1 thing you found interesting • Homework: Worksheet

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