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Objectives
Vocabulary
Assignments
Use transforma.ons using rules
Transforma.on, preimage, image
Honors: 1, 3, 5, 10, 15-‐17 Regular: 2, 4-‐5, 10, 15
• A transforma.on is a func.on that changes the posi.on, shape, and/or size od a figure • The input of a transforma.on od the preimage, like A • The output is the image, like A’ (A prime) • Transla.on, reflec.ons and rota.ons are three types of transforma.on.
Basic Transformation Vocabulary
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Explain 1: Rigid vs Nonrigid • Some transforma.ons preserve length and angle measure, others do not • A rigid mo.on changed posi.on without affec.ng size or shape of the figure. • Examples: transla.on, reflec.ons, and rota.ons
Steps: 1) Look for paSers in the coordinates 2) Compare lengths of the preimage and image of corresponding
segments 3) Compare angles of corresponding angles 47
Types of Transformation
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-‐Up -‐Down -‐Le[ -‐Right
-‐90° �-‐180° -‐270° -‐360°
-‐Clockwise -‐Counter-‐clockwise
We will discuss this later
Y-‐axis X-‐axis 𝑦=𝑥 𝑦=−𝑥
Decide if they are Rigid or NON-‐rigid
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Transforma7on Example
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Recall Finding Distance Comparing Distance: 𝐴𝐵→𝐴↑′ 𝐵′ 𝐵𝐶→𝐵↑′ 𝐶′ 𝐴𝐶→𝐴↑′ 𝐶′
The rule is: (𝑥,𝑦)→_________
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Recall Finding Distance
PREIMAGE IMAGE Distance P to Q Distance P’ to Q’
Distance P to R Distance P’ to R’
Distance Q to R Distance Q’ to R’
The rule is: (𝑥,𝑦)→_________
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Explain 2: Non Rigid Mo7ons • A nonrigid mo.on do not preserve distance between points.
• Examples: stretch, compression (dila.ons)
• To Describe dila.ons use this: • Ver.cal Stretch: Mul.plica.on on y. 𝑒𝑥: (𝑥,𝑦)−> (𝑥,2𝑦)
• Ver.cal Compression: Mul.plica.on on y. 𝑒𝑥: (𝑥,𝑦)−> (𝑥, 1/2 𝑦)
• Horizontal Stretch: Mul.plica.on on x. 𝑒𝑥: (𝑥,𝑦)−> (2𝑥,𝑦)
• Horizontal Compression: Mul.plica.on on x. 𝑒𝑥: (𝑥,𝑦)−> (1/2 𝑥,𝑦)
Steps: 1) Look for paSerns in the coordinates (usually mul.plica.on) 2) Compare lengths of the preimage and image of corresponding
segments
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The y-‐value is being mul.plied by ___
The new rule is: (𝑥,𝑦)→_________
Because this CHANGES sides, this is a _____________ transforma.on.
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1.3 Classwork • Honors: 1, 3, 5, 10, 15-‐17 • Regular: 2, 4-‐5, 10, 15 Reminders: q Summer Assignment Due Friday q Electronic Class Contract due Aug 23rd
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