Lesson 1: Scale Drawings
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1 Name: : Scale Drawings Learning Target I can create scale drawings of polygonal figures by the Ratio Method I can determine the distance a point moves from the center of dilation based on the scale factor Real Connection (2 minutes) A common feature on cell phones and tablets is the ability to scale, to or an image by putting a thumb and index finger to the screen and making a (to reduce) or movement (to enlarge) as shown in the diagram below. Opening Exercise To the right is a picture of a bicycle. Which of the images below appears to be a well-scaled image of the original? Explain why the other two images are not well scaled. Be specific
2 Name: What is a scale factor? (r) -The constant of proportionality by which all lengths are scaled. What happens, to an image, when the scale factor is equal to 1? What happens, to an image, when the scale factor is greater than 1? What happens, to an image, what the scale factor is between 0 and 1? The Notation for Dilation is: D O,r where O: and r: Definition: A dilation is a rule (a function) that moves points in the plane a specific distance along the ray that originates from a center O. What determines the distance a given point moves? 1. If r > 1 the dilation will push the point from the center. 2. If r = 1 the dilation will keep the point from the center of dilation 3. If 0 < r < 1 the dilation will pull the point the center. Example of Dilation For any other point P, D O,r (P) is the point P on the ray OP so that OP = r OP. Ratio Method to Dilate images with a scale factor ( 0 < r < 1 ) Example1. Given center O and triangle ABC, dilate the figure from Connect center O by a scale factor of r = 1. Label the dilated triangle A B C. 4 the center of dilation O to all vertices Measure the length of segments OA =, OB=, OC= Apply the dilation rule for each length and calculate OA =, OB =, OC = Remember your dilated points A,B,C will be on the same rays that connect the center of dilation to each vertices Measure each length and connect the new points, label the image A B C Find the following ratios OC OC = OB OB OA = = OA
3 Name: A line segment AB undergoes a dilation. Based on today s lesson, what will the length of the image segment A B if the scale factor is r? Angle CBA measures 78. After a dilation, what will the measure of C B A be? How do you know? Ratio Method to Dilate images with a scale factor ( r > 1 ) Example 2 Given center O and triangle ABC, dilate the triangle from center O with a scale factor r = 3. Measure the length of segments OA =, OB=, OC= Apply the dilation rule for each length and calculate OA =, OB =, OC = Find the following ratios OC OC = OB OB = OA OA = Set up an extended proportion of the corresponding lengths = = Using a ruler measure AB= BC = and AC = Using a ruler measure A B = B C = and A C = Set up an extended proportion of the corresponding side-lengths = = = Lesson Summary There are two properties of a scale drawing of a figure: 1. Corresponding angles are in measurement 2. Corresponding lengths, sides are in measurement.
4 Name: : Scale Drawings Classwork Exercise 1) Create a scale drawing/ dilation of the figure below about center O with scale factor r = 1 2. Exercise 2) Create a scale drawing of the figure below about center O and scale factor r = 3. Measure the length of OA : Measure the length of OA ' : What is the ratio of OA to OA? m A = 17, m B = 134, m C = 22, m D = 23 What will be the measures of m A = m B =, m C =, m D =
5 Name: Exercise 3) Dilate circle A, from center O at the origin by scale factor r = 3. Exercise 4. Use the ratio method to create a scale drawing about center O with a scale factor of r = 1 4. Give the proper notation of the Dilation:
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