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Texas Algebra I Review: Scale Factor Transformations Lesson

This lesson covers how to perform transformations on geometric figures with a scale factor in and out of the coordinate plane. Students will learn to determine the scale factor used to transform figures and explain the effects on perimeter, area, and volume. Topics include dilation and scale factors, with examples of enlargements and reductions using different scale factors. Students will practice dilations and analyze the impact on figure size. Additional exercises explore how dilations affect perimeter, area, and volume calculations.

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Texas Algebra I Review: Scale Factor Transformations Lesson

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  1. Texas Algebra I Review: Scale Factor

  2. Lesson Objectives: The student will be able to: Perform transformations on given geometric figures given a scale factor (both in and out of the coordinate plane) Determine the scale factor used to transform one figure to a similar one Explain the effect using a given scale factor to transform a given figure will have on the perimeter, area, or volume of the figure.

  3. Transformations • Dilation-a transformation in which a geometric figure is enlarged or reduced using a scale factor • Scale factor- the value the dimensions of a figure are multiplied by in order to make the figure larger or smaller

  4. Sample Dilationcoordinate plane • Suppose we wanted to dilate the figure to: • 3 times its size • 2/3 its size • Both cases are the same! Simply multiply each coordinate by the given sale factor.

  5. Enlargement First, we’ll enlarge the pre-image using the scale factor of 3: (-5,8)*3 = (-15, 24) (6,4)*3 = (18, 12) (-3, -5)*3 = (-9, -15) The image produced by this transformation will be 3 times as large as the original triangle.

  6. Reduction Now, we’ll reduce the pre-image using the scale factor of 2/3: (-5,8)*2/3 = (-10/3, 16/3) (6,4)*2/3 = (4, 8/3) (-3, -5)*2/3 = (-2, -10/3) The image produced by this transformation will be 2/3 as large as the original triangle.

  7. Enlargement and Reductionout of the plane Problem: Determine the scale factor used to dilate figure 1 to figure 2.

  8. Effect of dilations on Perimeter, Area, & Volume

  9. Lesson Objectives: The student will be able to: Perform transformations on given geometric figures given a scale factor (both in and out of the coordinate plane) Determine the scale factor used to transform one figure to a similar one Explain the effect using a given scale factor to transform a given figure will have on the perimeter, area, or volume of the figure.

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