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?
- rx-axis is (x,-y)
- ry-axis is (-x,y)
- BE CARFEFUL OF THE TWO ABOVE! THEY ARE OPPOSITE OF WHAT YOU'D PROBABLY THINK!!
- ry=x is (y,x)
- ry=-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 90o. You always rotate counter clockwise unless told otherwise.
- R90o is (-y,x)
- R180o is (-x,-y)
- R270o 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?
Dk 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 D3 o T(3,-6)
You must go backwards, so the translation in this case goes first, and then you dilate the image.