# Analytic geometry

The topic is divided into the following subtopics:
• Points and vectors
• Analytic geometry in a plane
• Analytic geometry in a space
• Conics

### Points and vectors

Part I:
• Points and vectors in plane and in space
• Length of a vector
• Operations with vectors – sum, scalar multiple
• Linear combination of vectors
• Linear dependence of vectors
• Line segment – center, length
• Triangle – centroid, centers of sides, lengths of sides, perimeter
Part II:
• Scalar product (dot product) of vectors in plane and in space
• Perpendicular vectors
• Angle of vectors
• Applications – plane shapes, solids in coordinate system
Part III:
• Vector product of vectors
• Area of a plane region, area of a face of a solid
• Volume of a solid (parallelepiped, pyramid, tetrahedron)
• Complex problems covering whole topic

### Analytic geometry in a plane

Part I:
• Line – parametric description, general equation, point-slope form equation
• Direction vector and normal vector of a line
• Line segment, half-line – parametric description
• Relative position of two lines
• Perpendicularity of lines
• Parallelity of lines
Part II:
• Distance of a point from a line
• Distance of two parallel lines
• Angle of two lines
• Triangle – medians, heights (altitudes), side perpendicular bisectors
• Line and point reflection, translation
Part III:
• Angles and distances – more complex problems
• Complex problems covering whole topic

### Analytic geometry in a space

Part I:
• Line – parametric description
• Plane - parametric description, general equation
• Intersection of two lines
• Intersection of a line and a plane
• Intersection of two planes
• Relative position of points, lines and planes
Part II:
• Intersection of two planes – more complex problems
• Perpendicularity of lines and planes
• Parallelity of lines and planes
• Angles of lines and planes
Part III:
• Complex problems on perpendicularity
• Point, line and plane reflection
• Distance of a point from a plane
• Distance of a point from a line
• Metric problems on solids

Part I: