Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Constructing the image of a figure
Construct transformed figures and describe compositions carrying one figure to another
Problem types
- Choose the transformations that map one figure to another
- Name the two motions that map one triangle to the next
- Name the image of a side after two reflections
Builds on
- What a transformation keeps
- Symmetries of a polygon · Earlier idea
A symmetry is a rotation or reflection that maps a figure onto itself. Mapping a figure onto a different position uses compositions of the same transformations.
Leads to
- Why every circle is similar to every other · See it applied
Mapping one circle onto another uses a translation followed by a dilation, which is a composition chosen like any other figure-to-image sequence.
Related skills
- How a dilation changes a figure · Related idea
A construction that maps one figure to another by a sequence including a dilation uses the dilation's scale factor and center.
- Shifts, stretches, and reflections of graphs · Related idea
A sequence of translations, reflections and dilations carries one figure to another, as a sequence of shifts, reflections and stretches carries one graph to another.
- Matrices as transformations of the plane · Related idea
Multiplying matrices composes transformations: the product AB applies B first and then A. This is the matrix form of carrying one figure to another by a sequence of moves.
- Translations, reflections, and rotations · Related idea
Plot transformed vertices using off-origin turns, reflections and compositions described geometrically (HSG.CO.A.5 and HSG.CO.B.6).
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