## Tuesday, August 7, 2007

### Geometry 10.7 Locus of points

Chapter 10.7 Locus:

I)Vocabulary:
A) Locus - in a plane is the set of all points in a plane that satisfy a given condition or a set of given conditions. The word locus is derived from the Latin word for location. The plural of locus is loci, pronounced "low-sigh"
- can be described as the path of an object moving in a plane.
B) Finding a locus
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 can recognize a pattern.
4) Draw the locus and describe it in words.

Examples:
1) Given a point C, what is the locus of points 3 inches from C?
When you draw this you will get: the locus of points is a circle with center point C and a radius of 3 inches.

2) Given line AB, what is the locus of points 2 cm from line AB?
the locus of points 2 cm from line AB is 2 lines parallel to AB on either side of line AB 2 cm from AB

3) Given lines AB and CD, what is the locus of points equidistant from lines AB and CD?
the locus of points is a line parallel to both AB and CD that is half way between the lines AB and CD.

4) Given ∠BAC, what is the locus of points equidistant from ray AB and ray AC?
the locus of points is the angle bisect of ∠BAC.

5)Given point A and point B, what is the locus of points equidistant from point A and point B?
the locus of points is the perpendicular bisector of line segment AB.

C) Earthquakes - the epicenter of an earthquake is the point on the Earth's surface that is directly above the earthquake's origin. A seismograph measures ground motion during an earthquake. The seismograph measures the distance to the epicenter, but not he direction to the epicenter. To locate the epicenter, readings from three seismographs in different locations are needed.

1) locating an epicenter:
You are given readings from 3 different seismographs:
1) point A(-2, 2) and distance to the earthquake is 3 miles
2) point B(4, -1) and distance to the earthquake is 6 miles
3) point C(1, -5) and distance to the earthquake is 5 miles

Drawing these three circles, the point of interception is the epicenter. This would be (-2, -1)