Presentation on theme: "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."— Presentation transcript:
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
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
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.
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).
A transformation maps the preimage to the image. Arrow notation ( ) is used to describe a transformation and primes (’) are used to label the image.
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’
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’
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.
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).
Assignment today is page 53: 8-17, 19-23 and 29-35. Remember that homework help is always available at http://www.thinkcentral.com/index.htm http://www.thinkcentral.com/index.htm Today’s keyword is “MG7 1-7”.