Download Math II – Transformation Geometry Vocab

Math II – Transformation Geometry Vocab
Vocabulary:
Preimage – the original figure in the transformation of a figure in a plane.
Image – the new figure that results from the transformation of a figure in a plane.
Isometry – a transformation that preserves size: preimage and image are congruent.
Mapping – an operation that matches each element of a set with another element, its image, in
the same set.
Transformation – the operation that maps, or moves, a preimage onto an image. Three basic rigid
transformations are reflections, rotations, and translations. A dilation is a non-rigid transformation (not
an isometry).
Translation – sliding a figure without changing the size or shape of figure
Reflection – creates symmetry in the coordinate plane
Dilations - a transformation that produces an image that is the same shape as the original, but is a
different size (similar figure, so NOT an isometry)
• Dilations are enlargements (“stretches”) or reductions (“shrinks”)
• Scale factors are applied to the pre-image to create the image
• We multiply points in the pre-image by the scale factor to create the image
• Find scale factor by dividing a side length in the image by the corresponding side in the pre-image
• Scale factors bigger than 1 result in enlargements
• Scale factors smaller than 1 but greater than 0 result in reductions
Rotation – turn a figure about a fixed point
** counterclockwise rotation **
Composite transformations – multiple transformations done on a figure
** first is on the pre-image, second is on the image, the third is on the second image. NEVER GO
BACK TO THE ORIGINAL!!
For the preimage point (𝑥, 𝑦):
Translations
(𝒙 + 𝒉, 𝒚 + 𝒌)
Rigid Transformations
Reflections
Rotations
About xAbout y-axis: Counterclockwise
Clockwise
axis:
(positive angles)
(negative angles)
(𝑥, −𝑦)
(−𝑥, 𝑦)
90°
(−𝑦, 𝑥)
−270°
(−𝑦, 𝑥)
About 𝑦 = 𝑥
About 𝑦 = −𝑥
180°
−𝑥, −𝑦
180°
−𝑥, −𝑦
(𝑦, −𝑥)
(−𝑦, −𝑥)
270°
𝑦, −𝑥
−90°
𝑦, −𝑥
Non-rigid
Dilations
(𝑘𝑥, 𝑘𝑦)