Curriculum placement
Geometry. This describes the skill, not a learner estimate.
How a dilation changes a figure
Investigate how dilation changes lengths lines and parallelism
Problem types
- Dilations: lengths, centers and what is kept
- Volumes of similar solids
- Equation of a line after a dilation centered at the origin
- Find the scale factor and center of a graphed dilation
- Equation of a line after a dilation about a stated center
- Surface-area ratio to length scale to volume
Builds on
Leads to
- Why every circle is similar to every other · See it applied
A dilation maps one circle onto any other, so all circles are similar.
- Theorems about similar triangles · See it applied
A dilation keeps ratios of lengths, which makes corresponding sides of similar triangles proportional.
- Volumes of cylinders, cones, pyramids, spheres · See it applied
A scale factor k multiplies lengths by k and volumes by k cubed, which models scaled solids.
Related skills
- Constructing the image of 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.
- What a transformation keeps · Related idea
Dilations keep angles and ratios of lengths but not lengths, a different set of invariants from rigid motions.
- Matrices as transformations of the plane · Related idea
A scale matrix is a dilation about the origin, which multiplies every length by the scale factor and every area by its square.
- Vectors and their components · Related idea
A dilation multiplies each position vector by the scale factor, as a scalar multiple scales a vector.
- Proving triangles similar · Shared foundations
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