TRANSFOMATIONAL GEOMETRY EXAM WITH QUIZ & ANS (100% SOLVED)
Transformation - ✔✔✔–T, from set A into set B, is a one-to-one mapping T of a A onto B
distance is preserved
- the pre-image is the figure before its been transformed
- the image is the figure once its been transformed
Isometry - ✔✔✔–a transformation T of A onto B that preserves distance/lengths
they are called rigid transformations
Congruent Segments - ✔✔✔–two segments where isometry exists
Plane Motions in R^2 - ✔✔✔–translation
rotation
reflection
glide-reflection
Translation in R^2 - ✔✔✔–a sliding of the figure so that it changes location, but retains shape,
orientation, and size
a correspondence between points and their image points so that each image point is the same
distance in the same direction from the original point
T(x, y) = (x + a, y + b)
translation: a segment is translated into - ✔✔✔–a parallel segment
, TRANSFOMATIONAL GEOMETRY EXAM WITH QUIZ & ANS (100% SOLVED)
all vectors connecting corresponding points - ✔✔✔–are equal
the inverse of a translation is - ✔✔✔–another translation the same distance in the opposite
direction
the product (composition) of translations is a - ✔✔✔–translation
the set of all translations forms - ✔✔✔–a group with identity under the zero vector
Rotation in R^2 - ✔✔✔–R(O, α) represents rotation through an angle of α about the point O
T(x, y) = (xcos(α) - ysin(α), xsin(α) + ycos(α))
a counterclockwise rotation is associated with a positive angle
rotation: a segment is usually - ✔✔✔–not parallel to its image
the inverse of a rotation R(O, α) is - ✔✔✔–the rotation R(O, -α)
the product (composition) of two rotations about the same point - ✔✔✔–is another rotation
about the same point through an angle that is the sum of the measures of the original two
angles
the set of all rotations about the same point form - ✔✔✔–a group of rotations (with identity
being the rotation about that point through an angle of measure 0°)
Transformation - ✔✔✔–T, from set A into set B, is a one-to-one mapping T of a A onto B
distance is preserved
- the pre-image is the figure before its been transformed
- the image is the figure once its been transformed
Isometry - ✔✔✔–a transformation T of A onto B that preserves distance/lengths
they are called rigid transformations
Congruent Segments - ✔✔✔–two segments where isometry exists
Plane Motions in R^2 - ✔✔✔–translation
rotation
reflection
glide-reflection
Translation in R^2 - ✔✔✔–a sliding of the figure so that it changes location, but retains shape,
orientation, and size
a correspondence between points and their image points so that each image point is the same
distance in the same direction from the original point
T(x, y) = (x + a, y + b)
translation: a segment is translated into - ✔✔✔–a parallel segment
, TRANSFOMATIONAL GEOMETRY EXAM WITH QUIZ & ANS (100% SOLVED)
all vectors connecting corresponding points - ✔✔✔–are equal
the inverse of a translation is - ✔✔✔–another translation the same distance in the opposite
direction
the product (composition) of translations is a - ✔✔✔–translation
the set of all translations forms - ✔✔✔–a group with identity under the zero vector
Rotation in R^2 - ✔✔✔–R(O, α) represents rotation through an angle of α about the point O
T(x, y) = (xcos(α) - ysin(α), xsin(α) + ycos(α))
a counterclockwise rotation is associated with a positive angle
rotation: a segment is usually - ✔✔✔–not parallel to its image
the inverse of a rotation R(O, α) is - ✔✔✔–the rotation R(O, -α)
the product (composition) of two rotations about the same point - ✔✔✔–is another rotation
about the same point through an angle that is the sum of the measures of the original two
angles
the set of all rotations about the same point form - ✔✔✔–a group of rotations (with identity
being the rotation about that point through an angle of measure 0°)
