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GeometryGeometry 10.7 Locus. GeometryGeometry Drawing a Locus that Satisfies One Condition A locus in a plane is a set of all points in a plane that satisfy.

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Presentation on theme: "GeometryGeometry 10.7 Locus. GeometryGeometry Drawing a Locus that Satisfies One Condition A locus in a plane is a set of all points in a plane that satisfy."— Presentation transcript:

1 GeometryGeometry 10.7 Locus

2 GeometryGeometry 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.

3 GeometryGeometry 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.

4 GeometryGeometry Ex. 1: Finding a Locus Draw a point C on a piece of paper. Draw and describe the locus of all points that are 3 inches from C.

5 GeometryGeometry Ex. 1: Finding a Locus Draw point C. Locate several points 3 inches from C. C

6 GeometryGeometry Recognize a pattern. The points lie on a circle. C

7 GeometryGeometry Ex. 1: Finding a Locus 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. C

8 GeometryGeometry Finding a Locus To find the locus of points that satisfy a given condition, use the following steps: 1.Draw any figures that are given in the statement of the problem. 2.Locate several points that satisfy the given condition. 3.Continue drawing points until you recognize the pattern. 4.Draw the locus and describe it in words.

9 GeometryGeometry 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.

10 GeometryGeometry 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?

11 GeometryGeometry Solution: The locus of all points that are equidistant from A and B is the perpendicular bisector of AB.

12 GeometryGeometry SOLUTION continued The locus of all points that are a distance of AB from B is the circle with center B and radius AB.

13 GeometryGeometry SOLUTION continued These loci intersect at D and E. So D and E are the locus of points that satisfy both conditions.

14 GeometryGeometry

15 GeometryGeometry

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