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MATH 3A CHAPTER 12 POWERPOINT PRESENTATION. GEOMETRY AND IMAGINATION. LEARNING TARGETS. AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: IDENTIFY HOW GEOMETRIC FIGURES INTERSECT IN SPACE. WRITE EQUATIONS FOR LOCI. CONNECT SIMPLE AND COMPOUND LOCI. DESCRIBE COMPOUND LOCI.

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learning targets
LEARNING TARGETS
  • AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:
  • IDENTIFY HOW GEOMETRIC FIGURES INTERSECT IN SPACE.
  • WRITE EQUATIONS FOR LOCI.
  • CONNECT SIMPLE AND COMPOUND LOCI.
  • DESCRIBE COMPOUND LOCI.
lines in the plane and in space
LINES IN THE PLANE AND IN SPACE
  • IN THE PLANE: FOR A 2-D FIGURE, IT IS EASY TO THINK ABOUT LINES LIKE A RADIUS OR A DIAMETER. THE LOCUS OF POINT FROM A GIVEN CENTER IS A CIRCLE.
  • IN SPACE: THE LOCUS OF POINTS IN SPACE AT EQUAL DISTANCES FROM A GIVEN POINT IS A SPHERE.
loci in the coordinate plane
Loci In The Coordinate Plane
  • Think of parallel lines, horizontal lines, vertical lines. When they are on a graph, the locations of the points can be used to solve many problems.
  • Finding a midpoint, the equidistant locus, perpendicular bisectors, locus of points that forma circle. All of this is how we discover the loci in the coordinate plane.
equation for a circle1
Equation for a Circle
  • r² = x² + y²
compound loci
COMPOUND LOCI
  • YOU HAVE LEARNED HOT TO VISUALIZE LOCI, NOW WE WILL LOOK AT LOCI THAT SATISFY MORE THAN ONE CONDITION AT A TIME CALLED COMPOUND LOCI.
can you find some other examples
Can You Find Some Other Examples
  • In machines
  • In buildings
  • In bridges
  • In cars, trucks, planes, ships, busses
  • In chemistry, medicine
  • In nature?????
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