10.7 Locus

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# 10.7 Locus - PowerPoint PPT Presentation

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 &amp; B AND Chapter 10 Review #1-32 all. .

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### 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.
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
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
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

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
• 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
• 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
• 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?
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
• 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 continued
• The reading from B tells you that the epicenter is one of the two points of intersection of A and B.
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
• 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?
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:
• 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.