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Dilations:
Dilations are mappings that deal with similarities not congruence. Rotations, reflections, translations are all congruence mapping.
If | k | > 1 then the dilation is called an expansion.
If | k | < 1 then the dilation is called an contraction.
Rotations:
Theorem:
Translation or Glide Transformations:
A translation or glide, is an isometry that glides all the points of a figure the same distance.
Theorem:
If a transformation T maps any point (x,y) to (x+a,y+b) then the transformation T is a translation.
Coordinate Geometry
Theorem 11.2 The Equation of a Circle.
The equation of a circle with its center at (a,b) and a radius r is:
r²= (x - a)² + (y - b)²
Slope of a line:
Theorem:
Coordinate Geometry
Spheres:
The Area and Volume of the Sphere:
A = 4pr
Areas and Volumes of Similar Solids:
Theorem:
If a : b is the scale factor of two figures then:
Cylinder and Cones:
Pyramids:
Point V in the figure is the vertex of the pyramid.
The segment perpendicular to the base from the vertex is the altitude and its length is the height h.
Regular Pyramids have:
Prisms:
Solids
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