
What is an image and a preimage?
An image is the object after the transformation, and the preimage is the image before.

What is an isometry?
A transfromation that preserves length and angle measure. It does not have to preserve orientation. It keeps the shape the same size and same shape.

What is a translation?
A sliding of points to same distance in the same direction. It is simply a slide. A translation is an isometry.

How do you perform a translation?
t_{(m,n)} is (x+m,y+n)

What is a reflection?
A transformation that reflects an image over a line like a mirror. It is an isometry.

How do you perform a reflection?
 r_{xaxis} is (x,y)
 r_{yaxis} is (x,y)
 BE CARFEFUL OF THE TWO ABOVE! THEY ARE OPPOSITE OF WHAT YOU'D PROBABLY THINK!!
 r_{y=x} is (y,x)
 r_{y=x} is (y,x)
 SImply flip the points. Count the boxes on a coordiante plane!

What is a rotation?
An isomtry that rotates the figure around the center of rotation. THis is always about the origin in geometry.

How do you perform a rotation?
 There are two ways, rotate the paper (But be carfeul not to make a mistake), or use the method: flip and negate the first! This means that you flip the coordinates and then negate the coordinate that is now first to go 90^{o}. You always rotate counter clockwise unless told otherwise.
 R_{90o} is (y,x)
 R_{180o} is (x,y)
 R_{270o} is (y,x)

What is a dilation?
A transformation that changes the size of the shape (shrink or grow).

How do you perform a dilation?
D_{k} is (kx,ky). In other words, just mulitply the scale factor to the coordinates.

What is glide reflection?
A reflection that is also translated so that it appears to slide after being reflected.

What do you know about compositions of transformations, like D_{3} ^{o}_{} T_{(3,6)}_{}
You must go backwards, so the translation in this case goes first, and then you dilate the image.

