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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.





More Intersect in the Real World


Can you find some other examples
Can You Find Some Other Examples Intersect in the Real World

  • In machines

  • In buildings

  • In bridges

  • In cars, trucks, planes, ships, busses

  • In chemistry, medicine

  • In nature?????


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