Geometry 7.1 Rigid Motion in a Plane. Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 2 Goals Identify the three basic rigid transformations.

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Presentation transcript:

Geometry 7.1 Rigid Motion in a Plane

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 2 Goals Identify the three basic rigid transformations. Use correct terminology in transformations.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 3 Transformations Reflections Rotations Translations

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 4 Transformations The “original” object is the preimage. The copy is the image. preimageimage

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 5 Preimage Image Translation

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 6 Reflection PreimageImage Line of Reflection

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 7 Rotation Preimage Images Center of Rotation

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 8 Labels If a preimage point is A, then the corresponding image point is A’. A’ is read “A prime”. Preimage  ABC is transformed to image  A’B’C’.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 9 Reflection Preimage Image A B C B’B’ C’C’ A’A’

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 10 Mapping A transformation is a mapping. If  RST is translated to  XYZ, we say “  RST is mapped onto  XYZ”. We write  RST   XYZ.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 11 Write the mapping for this diagram. A B C V N T 90° 60° 30° 90° 30° 60°  ABC   ______ VTN This mapping is arotation.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 12 ABCD  RSTV BADC  CD  AB  DA  TV RS VR SRVT This mapping is areflection.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 13 Isometry Iso = The same Metry = Measure Isometry means “The same measure”.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 14 Isometries preserve… segment length angle measure parallel lines distances Transformations that are isometries are called Rigid Transformations.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 15

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 16 Are all transformations also isometries? NO! A BC A' B'C'  ABC   A'B'C' Segment length not preserved. Angle measures not preserved. Orientation is preserved.

Monday, Nov 17, 2:41 PMGeometry 7.1 Rigid Motion in a Plane 17 The rest of this chapter will be done by construction methods.