Geometry Transformation Rules

use this to help you remember the rules for reflection, and rotations

When reflecting over the X-axis…

Change the sign of the Y-coordinate:

(x,y) —> (x,-y)

When reflecting over the Y-Axis…

Change the sign of the X-coordinate:

(x,y) —> (-x,y)

When reflecting over the X and Y axes

Change the signs of both coordinates:

(x,y) —> (-x,-y)

When reflecting over a line where Y= x (y=1x+0)…

Switch the coordinates:

(x,y) —> (y,x)

When reflecting over a line where y= # (horizontal line)

X-coordinate stays the same and locate equal distance from the line in the opposite direction

When reflecting over a line were x= # (vertical line)

Y-coordinate stays the same and locate equal distance from the line in the opposite direction

When reflecting over a line where y=-x (y=-1x+0)

Switch the coordinates and change both signs:

(x,y) —> (-y,-x)

When rotating 90° CCW (or 270° CW) around the origin…

(x,y) —> (-y,x)

When rotating 270° CCW (or 90° CW) around the origin…

(x,y) —> (y,-x)

When rotating 180° CCW (or 180° CW) around the origin…

(x,y) —> (-x,-y)

When rotating 360° CCW (or 360° CW) around the origin…

(x,y) —> (x,y)