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.

ABC A’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!

DEFG D’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

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).

7,1( )

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

Today’s keyword is “MG7 1-7”.