Geometric Transformation

types of geometric transformations

• translation

• reflection

• rotation

• dilation

• glide reflection

translation

moving a figure in the same direction without changing its size, shape, or orientation

pre-image

initial figure before translation

image

resulting figure after translation, add ‘ when indicating points

quadrants

right side - positive first

left side - negative first

translation rules on the coordinate plane

x axis - right is positive, left is negative
y axis - up is positive, left is negative

reflection

a figure is flipped across a line, resulting in a mirrored image of the original

rules on different types of reflection

rotation

turns a figure around the center of rotation

common angles

rules on different types of rotation

90 degrees CCW - X value doesn’t change when switched to Y value

dilation

changing the size of a figure by expansion, or contraction

scale factor

• the ratio between the pre image and the image, to see how much it changed in size

• denoted by r or k

formula: k = length of image / length of pre-image

dilation in enlarging when SF>1

multiply all the coordinates by the scale factor

dilation in shrinking when SF<1

multiply all the coordinates by the scale factor

glide reflection

• combines two transformations: reflection and translation

• translation first, then reflection