advanced geometry unit 3

issaquah highschool advanced geometry sedlacek

rotation

a turn around a fixed point called the center of rotation

the figure rotates at a specific angle and direction

though the figure can rotate around any fixed point, the most common center of rotation is the origin (0,0)

what way is rotations for a positive angle measure?

counter clockwise

what way is rotations for a negative angle measure?

clockwise

90 degree rotation

notation: r(90°,0) and r(-270°,0)

Rule: (x,y) → (-y,x)

180 degree rotation

notation: r(180°,0) and r(-180°,0)

Rule: (x,y) → (-x,-y)

270 degree counter clockwise rotation

notation r(270°,0) and r(-90°,0)

Rule: (x,y) → (y,-x)

translation

a transformation that maps points from a pre-image the same distance and direction to its image.

concept of a rigid motion

a combination of two or more rigid transformations in which the second rigid motion is performed on the image of the first rigid motion.

something that isnt a rigid motion is when the image gets bigger than the preimage

reflection

a flip over a line called the line of reflection.

each point and its image are the same distance from the line of reflection

a reflection is also and example of a rigid motion.

reflection: Rx-axis / Ry=0

rule: (x,y) → (x,-y)

reflection: Ry-axis / Rx=0

Rule: (x,y) → (-x,y)

Reflection: Ry=x

Rule: (x,y) → (y,x)

Reflection:Ry=-x

Rule: (x,y)→ (-y,-x)