Transformation Rules

Rotation 180 degrees about the origin

(x,y) goes to (-x,-y)

Reflection over y-axis

(x,y) goes to (-x,y)

Reflection over y = -x

(x,y) goes to (-y,-x)

Rotation 90 degrees CCW about the origin

(x,y) goes to (-y,x)

Dilation by a scale factor of a units

(x,y) goes to (ax,ay)

Translation

(x,y) goes to (x+a,y+b)

Reflection over x-axis

(x,y) goes to (x,-y)

Rotation 270 degrees CCW about the origin

(x,y) goes to (y,-x)

Rotation 90 degrees CW about the origin

(x,y) goes to (y,-x)

Reflection over y = x

(x,y) goes to (y,x)

Reflection

A transformation that "flips" a figure over a line of reflection.

Translation

A transformation that "slides" each point of a figure in a plane according to a common operation or rule.

Dilation

A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.

Isometry

A transformation that preserves size and shape. The image of a figure under an isometry is congruent to the original figure. Also called a rigid transformation

Rotation

A transformation that turns a figure about a fixed point through a given angle and a given direction.

Corresponding Angles

Angles that have the same relative positions in geometric figures.

If a is greater than 1, then the image is...

Enlarged

Similar Figures

Figures that have the same shape but not necessarily the same size. Corresponding angles are congruent but corresponding sides are proportional.

Congruent Figures

Figures that have the same size and shape

If a is less than 1, then the image is...

Reduced

Corresponding Lengths

Sides that have the same relative positions in geometric figures.

Angle of Rotation

The amount of rotation about a fixed point, given in degrees.

Transformation

The mapping, or movement, of all points of a figure in a plane according to a common operation.

Scale Factor

The ratio of any two corresponding lengths of two similar figures.

Reflection Line

a line that a figure is flipped across to create a mirror image of the original figure

Preimage

the original figure in a transformation