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rigid transformation

Rigid Transformations

TermDefinition
translation a slide described by length and direction
reflection a flip transformation of an object in a mirror line or reflection line
rotation a transformation in which a figure is turned or rotated about a point
centre of rotation the point around which an object can be rotated
dilation a transformation that changes the size of an object
line of symmetry a mirror line that reflects an object onto itself
rotational symmetry a figure that maps onto itself more than once in a complete turn
point symmetry rotational symmetry of order 2
tesselation an arrangement of shapes that completely covers the plane without overlapping
A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".
A reflection (flip) is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.
A translation (slide) is called a rigid transformation or isometry because the image is the same size and shape as the pre-image
Rotation ( flip) the point about which the object is rotated can be inside the figure or anywhere outside it.
Translation (x+h, y+k)
Reflection across the X- Axis (x,-y)
Reflection across the Y- Axis (-x,y)
Reflection across the Y- Axis (-x,y)
Reflection across y=-x (-y,-x)
90 degrees counterclockwise or 270 clockwise (-y,x)
180 degrees both ways (-x,-y)
270 degrees counterclockwise or 90 clockwise (y,-x)
4 Types of Transformations - Rotation - Reflection - Translation - Dilation
Translation A shift of a graph horizontally, vertically, or both, which results in a graph of the same shape and size, but in a different position.
Rotation Turning around an axis or center point.
Reflection A transformation that "flips" a figure over a mirror or reflection line.