10 7 locus l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
10.7 Locus PowerPoint Presentation
Download Presentation
10.7 Locus

Loading in 2 Seconds...

play fullscreen
1 / 27

10.7 Locus - PowerPoint PPT Presentation


  • 193 Views
  • Uploaded on

10.7 Locus. Geometry Mrs. Spitz Spring 2005. Objectives/Assignment. Draw the locus of points that satisfy a given condition. Draw the locus of points that satisfy two or more conditions. Assignment: Worksheet A & B AND Chapter 10 Review #1-32 all. .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '10.7 Locus' - oakley


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
10 7 locus

10.7 Locus

Geometry

Mrs. Spitz

Spring 2005

objectives assignment
Objectives/Assignment
  • Draw the locus of points that satisfy a given condition.
  • Draw the locus of points that satisfy two or more conditions.
  • Assignment: Worksheet A & B
  • AND Chapter 10 Review #1-32 all.
drawing a locus that satisfies one condition
A locus in a plane is a set of all points in a plane that satisfy a given condition or set of given condition. Locus is derived from the Latin Word for “location.” The plural of locus is loci, pronounced “low-sigh.”Drawing a Locus that Satisfies One Condition
drawing a locus that satisfies one condition4
A locus is often described as the path of an object moving in a plane. For instance, the reason many clock surfaces are circular is that the locus of the end of a clock’s minute hand is a circle.Drawing a Locus that Satisfies One Condition
ex 1 finding a locus8
Using a compass, draw the circle.

The locus of oints on the paper that are 3 inches from C is a circle with center C and radius of 3 inches.

Ex. 1: Finding a Locus

C

finding a locus
Finding a Locus

To find the locus of points that satisfy a given condition, use the following steps:

  • Draw any figures that are given in the statement of the problem.
  • Locate several points that satisfy the given condition.
  • Continue drawing points until you recognize the pattern.
  • Draw the locus and describe it in words.
loci satisfying two or more conditions
Loci Satisfying Two or More Conditions
  • To find the locus of points that satisfy two or more conditions, first find the locus of points that satisfy each condition alone. Then find the intersection of these loci.
ex 2 drawing a locus satisfying two conditions
Ex. 2: Drawing a Locus Satisfying Two Conditions
  • Points A and B lie in a plane. What is the locus of points in the plane that are equidistant from points A and B and are a distance of AB from B?
ex 3 drawing a locus satisfying two conditions
Ex. 3: Drawing a Locus Satisfying Two Conditions
  • Point P is in the interior of ABC. What is the locus of points in the interior of ABC that are equidistant from both sides of ABC and 2 inches from P? How does the location of P within ABC affect the locus?
solution16
The locus of points equidistant from both sides of ABC is the angle bisector. The locus of points 2 inches from P is a circle. The intersection of the angle bisector and the circle depends upon the location of P. The locus can be 2 points ORSOLUTION:
earthquakes
Earthquakes
  • The epicenter of an earthquake is the point on the Earth’s surface that is directly above the earthquake’s origin. A seismograph can measure the distance to the epicenter, but not the direction of the epicenter. To locate the epicenter, readings from three seismographs in different locations are needed.
earthquakes continued20
Earthquakes continued
  • The reading from B tells you that the epicenter is one of the two points of intersection of A and B.
earthquakes continued21
Earthquakes continued
  • The reading from C tell you which of the two points of intersection is the epicenter.

epicenter

ex 4 finding a locus satisfying three conditions
Ex. 4: Finding a Locus Satisfying Three Conditions
  • Locating an epicenter. You are given readings from three seismographs.
    • At A(-5, 5), the epicenter is 4 miles away.
    • At B(-4, -3.5) the epicenter is 5 miles away.
    • At C(1, 1.5), the epicenter is 7 miles away.
  • Where is the epicenter?
solution23
Solution:
  • Each seismograph gives you a locus that is a circle.
  • Circle A has center (-5, 5) and radius 4.
  • Circle B has center (-4, -3.5) and radius 5.
  • Circle C has center (1, 1.5) and radius 7.
  • Draw the three circles in a coordinate plane. The point of intersection of the three circles is the epicenter.
reminders
Reminders:
  • Test Tuesday/Wednesday
  • Sub on Thursday/Friday – I expect all of you to be nice or else. Definitions/Postulates for Chapter 11 are due beginning of next week.
  • You will be completing 11.1 with the sub.
  • Deficiencies are due by this Friday, but all work you wanted considered must already be in. I will enter these by Wednesday.
  • Algebra Review for Chapters 9 and 10 are extra credit, but you must show all work.