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Warm Up 1.2.Find the product of all the possible areas of a rectangle whose sides are natural numbers and whose perimeter is 14. Find the interior angle measure of the hands on a clock at 9:10 a.m. 145 degrees 720

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Vocabulary Cool fact of the day – American Institute of Mathematics is building a replica of the palace “Alhambra” (Grenada, Spain) in Morgan Hill … transformationreflection preimage rotation image translation

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The Alhambra, a 13th-century palace in Grenada, Spain, is famous for the geometric patterns that cover its walls and floors. To create a variety of designs, the builders based the patterns on several different transformations.

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A transformation is a change in the position, size, or shape of a figure. In what I can only describe as bizarre, the original figure is called the preimage while the resulting figure is called the image. A transformation could be a reflection, a rotation or a translation (slide).

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A transformation maps the preimage to the image. Arrow notation ( ) is used to describe a transformation and primes (’) are used to label the image.

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Identify the transformation. Then use arrow notation to describe the transformation. The transformation cannot be a reflection because each point and its image are not the same distance from a line of reflection. Similarly it is not a translation (or slide) because segment AB is not parallel to segment A’B’. It is a 90 degree clockwise rotation about the origin. ABCA’B’C’

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Identify the transformation. Then use arrow notation to describe the transformation. The transformation cannot be a translation (or slide) because each point and its image are not in the same relative position. It’s not a rotation either … It is a reflection across the x-axis … note that all corresponding points are the exact same distance from the x-axis! DEFGD’E’F’G’

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To find coordinates for the image of a figure in a translation, add a to the x-coordinates of the preimage and add b to the y- coordinates of the preimage. Translations can also be described by a rule such as (x, y) (x + a, y + b). Find the coordinates for the image of ∆ABC after the translation (x, y) (x + 2, y - 1). Draw the image.

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Lesson Quiz 2. What transformation is suggested by the wings of an airplane? 1. What transformation is suggested by the wings of an airplane? Reflection 2. Given points P(-2, -1) and Q(-1, 3), draw PQ and its reflection across the y-axis. 3. Find the coordinates of the image of F(2, 7) after the translation (x, y) (x + 5, y – 6).

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Assignment today is page 53: 8-17, and Remember that homework help is always available at Today’s keyword is “MG7 1-7”.

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