Topic 3 - transformations

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Presentation transcript:

Topic 3 - transformations

In this Chapter I can… 3-1: find a reflected image and write a rule of reflection 3-2: translate a figure and write a rule for translation 3-3: rotate a figure and write a rule for rotation 3-4: specify a sequence of transformations to transform figures 3-5: describe the transformations that carry a figure onto itself and identify the type of symmetry

3-1 Reflections Homework: 7-9,19-24

vocabulary Rigid Motion - a transformation that preserves side length and angle measurement

vocabulary Reflection – a transformation that reflects each point across a line (of reflection) A A B A B C D C C’ D’ C’ A’ A’ B’ A’ B’

Example ABC A (-5, 6) B (1, -2) C (-3, -4) 𝑅 (𝑥−𝑎𝑥𝑖𝑠) A’ (-5, -6)

Example ABC A (-5, 6) B (1, -2) C (-3, -4) 𝑅 (𝑦−𝑎𝑥𝑖𝑠) A’ (5, 6)

Example ABC A (-5, 6) B (1, -2) C (-3, -4) 𝑅 (𝑦=2) A’ (-5, -2)

3-1 Reflections Homework: 23, 25-28

example ABC A (-5, 3) B (-3, 7) C (1, 5) 𝑅 (𝑦=?) A’ (1, -3) B’ (5, -1)

Continued To find the line of reflection, first find the midpoints between the image and pre-image. 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡= 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡= −5+1 2 , 3+−3 2 = −2,0 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡= −3+5 2 , 7+−1 2 = 1,3 A (-5, 3), B (-3, 7), C (1, 5) A’ (1, -3), B’ (5, -1), C’ (3, 3)

continued Next, use the 2 points to determine the line of reflection. 𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = 3−0 1−−2 = 3 3 =1 Point-Slope Form Slope Intercept Form 𝑦=𝑚𝑥+𝑏 3=1 1 +𝑏 𝑏=2 𝑦=𝑥+2 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) 𝑦−0=1(𝑥+2) 𝑦−3=1(𝑥−1)