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

MATH 3A CHAPTER 12 POWERPOINT PRESENTATION

GEOMETRY AND IMAGINATION


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.


Examples lines in the plane

EXAMPLES:LINES IN THE PLANE


Lines in space

LINES IN SPACE


Planes that interesect

PLANES THAT INTERESECT


Parts of a sphere

PARTS OF A SPHERE


Cylinders intersected by a plane

CYLINDERS (Intersected by a plane)


More pictures

More Pictures


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.


Examples perpendicular bisector and midpoint

Examples – Perpendicular Bisector and Midpoint


Loci for a circle

Loci for a Circle


Equation for a circle

Equation for a Circle


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.


Loci in various shapes

LOCI IN VARIOUS SHAPES


Loci in space

Loci in Space


Now use your imagination to figure out how shapes intersect in the real world

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


Math 3a chapter 12 powerpoint presentation

More


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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