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Dilations

Dilations. Mr. Pearson Inman Middle School 3.2.11 . Objectives. Determine whether a dilation is an enlargement, a reduction, or a congruence transformation enlargement – image has increased in size scale factor is greater than 1 reduction – image has decreased in size

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Dilations

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  1. Dilations Mr. Pearson Inman Middle School 3.2.11

  2. Objectives Determine whether a dilation is an enlargement,a reduction, or a congruence transformation enlargement – image has increased in size scale factor is greater than 1reduction – image has decreased in size scale factor is between a fraction or decimal greater than 0 but less than 1. congruence transformation – image stayed the same scale factor is exactly 1.

  3. Vocabulary • Dilation – a transformation that may change the size of a figure • Scale Factor – the ratio between the original and new image. Most dilations in coordinate geometry use the origin, (0,0), as the center of the dilation.

  4. Dilations (D) involve multiplication LOCATE POINT A . The Ordered Pair given is (2,3). Break the ordered pair down into its two parts: X = 2 Y = 3 ________________________ DILATION is 4, which means enlarging the distance from the origin by 4 times. Multiply 2 x 4 = 8 Multiply 3 x 4 = 12 This give you your new ordered pair for A’. (8, 12)

  5. DILATIONS: What is the scale factor ?ENLARGEMENT

  6. DILATIONS: What is the scale factor ? REDUCTION

  7. y x Dilations Five hexagons that are each 50% reduction (1/2) of the size of the one before it. Scale factor is ½, and the center point is the origin (center of the figures)

  8. Example 5-3b COORDINATE GEOMETRY Triangle ABC has vertices A(–1, 1),B(2, –2), and C(–1, –2). Find the image of ABCafter a dilation centered at the origin with a scale factor of 2. Sketch the pre-image and the image. Answer: A'(–2, 2), B'(4, –4), C' (–2, –4)

  9. Answer: reduction Example 5-4b Determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. a. b. Answer: 2; enlargement

  10. MULTIPLE-CHOICE TEST ITEMStephanie built a frame for a photograph that is 20 centimeters by 25 centimeters. The frame measures 40 cm by 50 cm. Which scale factor did she use? A 2 B 3 C D Example 5-5a

  11. MULTIPLE-CHOICE TEST ITEMRuben is making a scale drawing of the front of his house. His house is 48 feet wide and 30 feet high at its highest point. Ruben decides on a dilation reduction factor of What size poster board will he need to make a complete drawing? A 19 in. by 26 in. B 22 in. by 30 in. C 20.5 in. by 28 in. D 16 in. by 29 in. Example 5-5b Answer: B

  12. DILATIONS REVIEW + ASSIGNMENTS • Review: • Dilations can be • enlargements, (scaling factor > 1) • reductions, (scaling factor < 1) • congruence transformations (scaling factor = 1) • Homework: Finish classwork on dilations. • GPS TASK (SHADOW MATH is due Friday)

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