Math 2 Transformations

Transformation

An operation that changes a geometric figure's size, location, or orientation.

image

The resulting figure after a transformation

preimage

The original figure before a transformation

Translation

A transformation that "slides" each point of a figure the same distance in the same direction.

Reflection

A transformation that "flips" a figure over a mirror or reflection line.

Rotation

A transformation in which a figure is turned about a fixed point

Translation rule

(x,y) ----> (x + h, y + k)

Reflection across x-axis rule

(x,y) ----> (x,-y)

Reflection across y-axis rule

(x,y) ----> (-x,y)

Reflection across y = x rule

(x,y)---->(y,x)

Reflection across y = -x rule

(x,y)---->(-y,-x)

Reflection through the origin rule

(x,y)---->(-x,-y)

Dilation Rule

(x,y) -----> k(x,y) or (kx, ky)

Rotation 90 degrees rule

(x,y)----->(-y,x)

Rotation 270 degrees rule

(x,y)----->(y,-x)

Rotation 180 degrees about the origin Rule

(x,y) ----->(-x,-y)

Congruent

figures that have the same shape and size

Isometry

A map which preserves distances between points, aka a congruence transformation

Similar

figures that have the same shape and proportional size

Scale Factor

A number which scales, or multiplies, some quantity.

clockwise rotation

right turn

counterclockwise rotation

left turn