How Do We Use The Other Definitions Of Transformations?

Isometry - length is preserved - the
figures are congruent.

Direct Isometry - orientation is preserved - the order of the lettering in the
figure and the image are the same, either both clockwise or both
counterclockwise.

Opposite Isometry - orientation is not preserved - the order of the lettering is
reversed, either clockwise becomes counterclockwise or counterclockwise
becomes clockwise.

Orientation- Refers to the arrangement of points relative to the one another, after a transformation has occured.

Line Reflection (Opposite Isometry)

-Keeps Distance, Angle Measure, & Parrellism.

-Reverse Orientaton

Point Reflection (Direct Isometry)

-Keeps Distance, Angle Measure & Parrellism.

-Same Orientation

Translations(Direct Isometry)

-Keeps Distance, Angle Measure & Parrellism.

-Same Orientation.

Rotations (Direct Isometry)

-Keeps Distance, ANgle Measure & Parrellism.

-Same Orientation.

Diolation(Not Isometry)

-Keeps Angle Meauser & Parrellism.

-Lengths Not Same.

Great! Now Solve The Following Problem:

Which of the following transformations creates a figure that is similar (but not congruent) to the original figure? I. translation II. rotation III. dilation

[1] I only [2] II only [3] III only [4] II and III

How Do We Graph Rotations?

-A rotation is a transformation that turns a figure about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. (notation R_degrees )

-An object and its rotation are the same shape and size, but the figures maybe turned in different directions.

Rotation of 90°:

Rotation of 180°:

Rotation of 270°:

-When working in the coordinate plane, assume the center of rotation to be the origin unless told otherwise. A positive angle of rotation turns the figure counterclockwise, and a negative angleof rotation turns the figure in a clockwise direction.

Congratulations! You now know how to graph rotations. You can now try the following problem?

Rotate the triangle 90 degrees.

How Do We Graph Dilations?

-A dilation is a transformation (notation ) that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.

-The description of a dilation includes the scale factor.

*If the scale factor is > than 1, than the image will stretch.

*If the scale factor is > than 0 and < than 1, the image will shrink.

-To find the dimensions of the dilated image, multiply the dimensions of the original image by the scale factor.

PROBLEM: Draw the dilation image of pentagonABCDE with the center of dilation at the origin and a scale factor of 1/3. OBSERVE: Notice how EVERY coordinate of the original pentagon has been multiplied by the scale factor (1/3). HINT: Multiplying by 1/3 is the same as dividing by 3! -Congratulations! You now know how to graph dilations. You can now try solving the following problem: What are the coordinates of the point (2,-4) under the dilation D(-2)?

Being Forced To Create This

Just Made This Blog...Yay -_-