transformations on a coordinate plane

transformation

function that results in the change in position, size, or orientation of a figure, maps initial image to final image

preimage

initial image

image

final image

image

final image

1. translation

2. reflection

3. rotation

4. dilation

type of transformation

translation

figure can be slid in any direction

reflection

figure can be flipped over a line

rotation

figure can be turned around a point

dilation

figure can be enlarged or reduced in size

coordinate notation for translation

1. in x-axis

2. in y-axis

3. in origin

4. in y=x

5. in y=-x

6. in y=k or x=k

kind of reflection

(x,y) → (x,-y)

if reflection is on the x-axis

(x,y) → (-x,y)

if reflection is on the y-axis

(x,y) → (-x,-y)

if reflection is on the origin

(x,y) → (y,x)

if reflection is y=x

(x,y) → (-y,-x)

if reflection is y=-x

line of symmetry

line that folds two halves that match exactly

glide reflection

parallel to the line of translation

rotation

set of points are turned at an angle about a fixed point

counter and clockwise rotation

1. R 90 / R -90

2. R 180/ R -180

3. R 270/ R -270

4. R 360/R -360

kinds of rotation

(x,y) → (-y,x)

R 90 / R -90

(x,y) → (-x,-y)

R 180/ R -180

(x,y) → (y,-x)

R 270/ R -270

(x,y) → (x,y)

R 360/R -360