Locus of a Circle

Objectives:  Students will understand the definition of locus and how to find the locus of points given certain conditions.

Lesson:  Begin by having the students discuss their definition of a locus.  After the discussion, provide a formal definition of locus and discuss how to find the locus.  Finally, have the students work through an activity concerning the concept of locus.

In a plane, the locus is the set of all points in a plane that satisfy a given condition or a set of given conditions.  It is the also thought of as the of an object moving in a plane.

To find the locus for a given set of conditions, begin by drawing any figures or points given by the conditions.  Then begin drawing any points that would satisfy the conditions described.  Finally use this set of points to find the pattern under the given conditions and describe, in words, this pattern which is the locus.

The following activity can be done as an in class activity with ruler, compass, pencil, and graph paper.  For the in class version in Word format click here, for the GSP sketches of this activity click here.

Activity:  Finding the Locus

Find the locus of points that are a distance of A away from point B.

Find the locus of points that are equidistant from the points A and B.

Find the locus of points that are equidistant from the points A and B as well as equidistant from the point B.

Bob is trying to find the epicenter of the earthquake that occurred yesterday.  The epicenter of an earthquake is the point on the earths surface vertically above the origin of the earth quake.  He has information from three different seismographs from three different locations around the area in which the earth quake occurred.  The seismographs measure the distance from the actual seismograph itself to the epicenter, but they can not tell the direction in which the epicenter is located.  Bob must use the information gathered from the seismographs to help him find the epicenter of the earthquake.  He knows that the distance from the first seismograph to the epicenter is 5 miles, the distance from the second seismograph to the epicenter is 13 miles, and the distance from the third seismograph to the epicenter is 10 miles.  Bob also knows that if his office is located at the origin, the first Seismograph is located at the point (-1, 7), the second seismograph is located at the point (-3, -9), and the third seismograph is located at the point (8, -5).  Use this information to help Bob find the epicenter of the earthquake.

Conclusion:  Have the students discuss the answers that they found for each problem and how they found each answer.

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