Math 3a chapter 12 powerpoint presentation
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MATH 3A CHAPTER 12 POWERPOINT PRESENTATION PowerPoint PPT Presentation


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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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MATH 3A CHAPTER 12 POWERPOINT PRESENTATION

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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.


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.


EXAMPLES:LINES IN THE PLANE


LINES IN SPACE


PLANES THAT INTERESECT


PARTS OF A SPHERE


CYLINDERS (Intersected by a plane)


More Pictures


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.


Examples – Perpendicular Bisector and Midpoint


Loci for a Circle


Equation for a Circle


Equation for a Circle

  • r² = x² + y²


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.


LOCI IN VARIOUS SHAPES


Loci in Space


Now – Use Your Imagination to Figure Out How Shapes Intersect in the Real World


More


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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