Pre- Algebra Periods: 1, 2, & 4

Transforming geometry, 9-8, 9-9, & 9-10

Rigid Motions:
Translations (slides)
Rotations (turns)
Reflections (flips)

Translations 9-8

You can move pattern blocks by sliding them, flipping them, or turning them. Each of these moves is a transformation.
Sometimes called a slide. Moves a figure - Doesn't change the shape or size
A translation is a transformation that moves points in the same distance and in the same direction. A figure and its translated image are congruent. You can see examples of translations in wallpaper, fabric and wrapping paper.
The figure you get after a transformation is called the image.
To name the image of a point, you use the prime notation, Point A and its image Point A^’
After the figure is translated (moved), it is then called the image and you use ' (the prime notation)
So triangle ABC once it's moved up 2 spaces is now named ABC'

You can describe a transformation using arrow notation, which describes the mapping of a figure onto its image. A --> A^’
You can also use arrow notation to write a general rule that describes a transformation.

So... If point A is (3,5)----> A' is (5,1)
(A prime)
Write an equation.
Ask yourself, what do you have to do to X as 3 to get X' as 5?
And what do you have to do to Y as 5 to get Y' as 1

(X,Y)---> (X + 2, Y - 4) then you have A' as (5,1) and you proved it.


Symmetry 9-9

Symmetry means that if you divide a figure in half, both halves look exactly the same
Line of symmetry: where you can "fold" the figure and have it exactly the same
Figures can have 0 or more lines of symmetry
A random drawing would probably have no lines of symmetry
A butterfly has one line of symmetry
A rectangle has 2 lines of symmetry
A square has 4 lines of symmetry
A circle has infinite lines of symmetry (you can rotate it infinitely and divide it in half)

A figure has reflective symmetry when one half is a mirror image of the other half. A line of symmetry divides a figure with reflectional symmetry into two congruent halves.

Again, Reflections (flips)

Line of symmetry---> Fold Figure
Reflection Reflection is sometimes called a flip of the figure
The figure flips over a LINE OF REFLECTION
For example, if a triangle is in Quadrant I, it may flip over the y axis into Quadrant II
(the right side of the triangle is now the left side)
Or it may flip over the x axis into Quadrant IV
(the top of the triangle is now the bottom)
Or it may flip over any other line like y = x. This is more complicated to understand!





Rotation 9-10

This transformation takes a figure and TURNS IT
about a point called the CENTER OF ROTATION.
The angle of turning is called the ANGLE OF ROTATION.
The two most common angles: 90 degrees and 180 degrees

If you are going to rotate 90 degrees the rule is this

The Value of X Becomes the opposite of the Y Value & the Y value becomes what the value of x was.

EX: (X,Y)--->(-Y, X)

(5,4) rotated 90 degrees would be (-4,5)
(5,4)---> (-4,5)

If you rotate 90 degrees a figure in quadrant I it would rotate into quadrant II
I-->II
II-->III
III-->IV
IV-->I

The rotation is one quadrant over-- counterclockwise

If you are going to rotate 180 degrees the rule is this
(X,Y)--->(-X,-Y)
180 degrees: ends up in the opposite quadrant (I goes to III , II goes to IV and so on)
The image is: (x, y) goes to (-x, -y) SAME NUMBERS...OPPOSITE SIGNS!



submitted by Lorenzo