20 8β’3 -1 6 A Story of Ratios 15 Homework Helper G8-M3-Lesson 1: What Lies Behind βSame Shapeβ? 1. Let there be a dilation from center ππ. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² , and π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² . Examine the drawing below. What can you determine about the scale factor of the dilation? I remember from the last module that the original points are labeled without primes, and the images are labeled with primes. The dilation must have a scale factor larger than ππ, ππ > ππ, since the dilated points are farther from the center than the original points. 2. Let there be a dilation from center ππ with a scale factor ππ = 2. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² , and π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² . |ππππ| = 1.7 cm, and |ππππ| = 3.4 cm, as shown. Use the drawing below to answer parts (a) and (b). The drawing is not to scale. I know that the bars around the segment represent length. So, |ππππβ² | is said, βThe length of segment ππππ prime.β a. b. Use the definition of dilation to determine |ππππβ² |. We talked about the definition of dilation in class today. I should check the Lesson Summary box to review the definition. |πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|; therefore, |πΆπΆπΆπΆβ² | = ππ β (ππ. ππ) = ππ. ππ and |πΆπΆπΆπΆβ² | = ππ. ππ ππππ. Use the definition of dilation to determine |ππππβ² |. |πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|; therefore, |πΆπΆπΆπΆβ² | = ππ β (ππ. ππ) = ππ. ππ and |πΆπΆπΆπΆβ² | = ππ. ππ ππππ. Lesson 1: © 2015 Great Minds eureka-math.org G8-M3-HWH-1.3.0-09.2015 What Lies Behind βSame Shapeβ? 1 20 8β’3 -1 6 A Story of Ratios 15 Homework Helper 3. Let there be a dilation from center ππ with a scale factor ππ. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(π΅π΅) = π΅π΅β² , π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(πΆπΆ) = πΆπΆ β² , and |ππππ| = 10.8 cm, |ππππ| = 5 cm, and |ππππβ² | = 2.7 cm, as shown. Use the drawing below to answer parts (a)β(c). a. Using the definition of dilation with |ππππ| and |ππππβ² |, determine the scale factor of the dilation. |πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|, which means ππ. ππ = ππ β (ππππ. ππ), then ππ. ππ = ππ ππππ. ππ ππ = ππ ππ Use the definition of dilation to determine |ππππ |. Since the scale factor, ππ, ππ ππ is , ππ then |πΆπΆπΆπΆβ² | ππ = ππ |πΆπΆπΆπΆ|; therefore, |πΆπΆπΆπΆβ² | = ππ β ππ = ππ. ππππ, and |πΆπΆπΆπΆβ² | = ππ. ππππ ππππ. Lesson 1: © 2015 Great Minds eureka-math.org G8-M3-HWH-1.3.0-09.2015 What Lies Behind βSame Shapeβ? equality, ππ Since |ππ β²| = ππ|ππ |, then by the multiplication property of ππ b. β² οΏ½πππ΅π΅β² οΏ½ |ππππ| = ππ. 2
© Copyright 2024 Paperzz