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Topic: Analytic geometry 

Mathematics

 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level IV (Grade 9-12)
   Benchmark 1.Understands that objects and relations in geometry correspond directly to objects and relations in algebra (e.g., a line in geometry corresponds to a set of ordered pairs satisfying an equation of the form ax + by = c)
    Knowledge/skill statements
     1.Understands a line in geometry corresponds to a set of ordered pairs
     2.Understands the connections between algebra and geometry
     3.Knows that ax + by = c is the general equation for a line
     4.Understands the concept of a coordinate plane
     5.Knows that geometric figures can be described algebraically
   Benchmark 3.Uses synthetic (i.e., pictorial) representations and analytic (i.e., coordinate) methods to solve problems involving symmetry and transformations of figures (e.g., problems involving distance, midpoint, and slope; determination of symmetry with respect to a point or line)
    Knowledge/skill statements
     1.Uses synthetic geometric models to solve slope problems
     2.Uses synthetic geometric models to solve line symmetry problems
     3.Uses synthetic geometric models to solve point symmetry problems
     4.Uses synthetic geometric models to solve distance problems
     5.Uses synthetic geometric models to solve midpoint problems
     6.Understands the concept of a synthetic model (i.e., a pictorial representation)
     7.Uses analytic methods to solve slope problems
     8.Uses analytic methods to solve line symmetry problems
     9.Uses analytic methods to solve point symmetry problems
     10.Uses analytic methods to solve distance problems
     11.Uses analytic methods to solve midpoint problems
  Level V (Grade (College Readiness))
   Benchmark 5.Uses algebraic methods to solve geometric problems
    Knowledge/skill statements
     1.Translates geometric shapes into algebraic equations
     2.Translates algebraic equations into geometric shapes