GeometryGeometry 10.7 Locus Geometry Mrs. Spitz Spring 2005.

Slides:

Advertisements

Similar presentations

GeometryGeometry 10.6 Equations of Circles Geometry Mrs. Spitz Spring 2005.

Advertisements

GEOMETRY Circle Terminology.

PROPERTIES FOR UNDERSTANDING AND USE Arcs and Chords.

Chapter 12.1 Common Core – G.C.2 Identify and describe relationships among inscribed angels, radii, and chords…the radius of a circle is perpendicular.

CIRCLES Chapter 10.

Chapter 5 Properties of Triangles Perpendicular and Angle Bisectors Sec 5.1 Goal: To use properties of perpendicular bisectors and angle bisectors.

5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.

5.1: Perpendicular Bisectors

Using properties of Midsegments Suppose you are given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?

Bell Problem. 5.2 Use Perpendicular Bisectors Standards: 1.Describe spatial relationships using coordinate geometry 2.Solve problems in math and other.

Locus Page 2 & Given: A and B Find points equidistant from these two fixed points Find points equidistant from these two intersecting lines Find.

Geometry 10.7 Locus not Locust!. June 8, 2015Geometry 10.7 Locus2 Goals  Know what Locus is.  Find the locus given several conditions.

Intersection of Loci You will be given a few conditions and asked to find the number of points that satisfy ALL the conditions simultaneously. The solution.

Compound Locus Page 7-9. Steps for solving compound loci problems: 1.Find all possible points for first locus. Mark with dotted line or smooth curve.

10.5 Segment Lengths in Circles Geometry Mrs. Spitz Spring 2005.

9.2 The Pythagorean Theorem Geometry Mrs. Spitz Spring 2005.

GeometryGeometry 10.2 Arcs and Chords Geometry Mrs. Spitz Spring 2005.

Geometry Equations of a Circle.

GeometryGeometry Lesson 75 Writing the Equation of Circles.

CIRCLES Unit 9; Chapter 10. Tangents to Circles lesson 10.1 California State Standards 7: Prove and Use theorems involving properties of circles. 21:

1. Dan is sketching a map of the location of his house and his friend Matthew’s house on a set of coordinate axes. Dan locates his house at point D(0,0)

Compound Locus Page 7-9.

Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.

Aim: How can we review what a locus is and its rules? Do Now: What is the definition of a locus? A locus is a set of points that satisfies a certain condition.

Key Term: Epicenter. Locating the Epicenter Please turn to page 116 in your textbook. Epicenter The point on Earth’s surface directly above the focus.

EXAMPLE 4 Graph a circle The equation of a circle is (x – 4) 2 + (y + 2) 2 = 36. Graph the circle SOLUTION Rewrite the equation to find the center and.

Geometry CH 1-6 Basic Constructions End of Lecture / Start of Lecture mark.

Locus – Equation of Circle Page 5. Essential Question: What is the difference between a linear equation, quadratic equation, and the equation of a circle?

SHS Analytic Geometry Unit 5. Objectives/Assignment Week 1: G.GPE.1; G.GPE.4 Students should be able to derive the formula for a circle given the Pythagorean.

10.2 Arcs and Chords Geometry.

10.3 Arcs and Chords Geometry.

AIM: LOCUS By: Nick Woodman & Robert Walsh.  Locus - in a plane is the set of all points in a plane that satisfy a given condition or a set of given.

10.1 Tangents to Circles.

Section 10-6 The Meaning of Locus. Locus A figure that is the set of all points, and only those points, that satisfy one or more conditions.

GeometryGeometry 6.2 Arcs and Chords Homework: Lesson 6.2/1-12,18 Quiz on Friday on Yin Yang Due Friday.

Topic, Question, & Hypothesis IS DUE TOMORROW!!!!!

BY WENDY LI AND MARISSA MORELLO

Lesson 14.1 Locus By the end of this lesson you will be able to use the 4 step procedure to solve locus problems.

GeometryGeometry 10.6 Equations of Circles Geometry.

Arcs and Chords Geometry.

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.

What is a locus? What is the relationship between a perpendicular bisector of a segment and the segment’s endpoints? What is the relationship between the.

1 LC.01.2 – The Concept of a Locus MCR3U - Santowski.

10-6 – 10-8 Locus, Loci, and Locus construction Locus is a set of points that satisfy a condition or a set of conditions. Loci is plural. Key words: In.

10.7 Locus Geometry.

Eleanor Roosevelt High School Chin-Sung Lin. Mr. Chin-Sung Lin ERHS Math Geometry.

Geometry Sections 5.1 and 5.2 Midsegment Theorem Use Perpendicular Bisectors.

Unit 1 Review Geometry 2010 – The Buildin g Blocks The ‘Seg’ Way Is that an angle? Point of that Triangle ! ConstructSolv e it! We All Like Change.

Chapter 10.7 Notes: Write and Graph Equations of Circles

GeometryGeometry Equations of Circles. GeometryGeometry Objectives/Assignment Write the equation of a circle. Use the equation of a circle and its graph.

10.1 TANGENTS TO CIRCLES GEOMETRY. OBJECTIVES/ASSIGNMENT Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment:

GeometryGeometry Lesson 6.1 Chord Properties. Geometry Geometry Angles in a Circle In a plane, an angle whose vertex is the center of a circle is a central.

GeometryGeometry 12.3 Arcs and Chords Geometry. Geometry Geometry Objectives/Assignment Use properties of arcs of circles, as applied. Use properties.

AIM : How do we find the locus of points ? Do Now: If all of your classmates were to stand 5 feet away from you, what geometric shape would your classmates.

Warm-Up Exercises ANSWER 17 ANSWER 13 Evaluate each expression. 1. (10 – 2) 2 + (8 + 7) 2 2. (–3 – 2) 2 + (–8 – 4) 2.

Advanced Algebra H Notes Section 9.3 – Graph and Write Equations of Circles Objective: Be able to graph and write equations of circles. A _________ is.

GeometryGeometry Equations of Circles Section 11.7.

Constructions Bisect – To divide something into two equal parts Perpendicular – Lines that intersect to form right angles. Today’s constructions: –Bisect.

10.1 Tangents to Circles Geometry Ms. Reser.

Chapter 5.1 Segment and Angle Bisectors

Evaluate each expression.

Geometry Mrs. Padilla Spring 2012

1.2 Informal Geometry and Measurement

Geometry 10.7 Locus not Locust!.

Objectives/Assignment

Geometry Equations of Circles.

Geometry Mrs. Spitz Spring 2005

Geometry Mrs. Spitz Spring 2005

Presentation transcript:

GeometryGeometry 10.7 Locus Geometry Mrs. Spitz Spring 2005

GeometryGeometry 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.

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. Locus is derived from the Latin Word for “location.” The plural of locus is loci, pronounced “low-sigh.”

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.

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.

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

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

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

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.

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.

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?

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

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.

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

GeometryGeometry 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?

GeometryGeometry SOLUTION: 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 OR

GeometryGeometry SOLUTION: OR 1 POINT OR NO POINTS

GeometryGeometry 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.

GeometryGeometry Earthquakes continued The reading from seismograph A tells you that the epicenter is somewhere on a circle centered at A.

GeometryGeometry Earthquakes continued The reading from B tells you that the epicenter is one of the two points of intersection of A and B.

GeometryGeometry Earthquakes continued The reading from C tell you which of the two points of intersection is the epicenter. epicenter

GeometryGeometry 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?

GeometryGeometry 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.

GeometryGeometry Solution: Draw the first circle.

GeometryGeometry Solution: Draw the second circle.

GeometryGeometry Solution: Draw the third circle. The epicenter is about (-6, 1).

GeometryGeometry 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.