Pre Algebra Period 2

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. Choose corresponding points on a figure and its image. Subtract the coordinates of the pre image from the coordinates of the image.
An arrow pointing to the right tells what the translation is.
So if point A (3, 5) is moved to (5, 1), the notation is A(3, 5) arrow A'(5, 1)
To write the rule of translation:
Use (x, y) then arrow to the right then (x + or - translation number, y + or - translation number)
So for the translation of A above:
(x, y) arrow to the right (x + 2, y - 4)

Symmetry and Reflection 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.


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!


A Reflection flips a figure over a line of reflection. The reflected figure, or image, is congruent to the original figure, called a pre image.

In any to these cases, the vertices of the triangle are not in the same place as before
(as they would be in a translation or slide)


Rotation
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:

180 degrees: ends up in the opposite quadrant (I goes to III , II goes to IV)
The image is: (x, y) goes to (-x, -y) SAME NUMBERS...OPPOSITE SIGNS!

90 degrees: ends up in the next quadrant over counterclockwise
The image is (x, y) goes to (-y, x).