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 conditions. The word locus is derived from the Latin word for location.

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.

Types of Loci

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.

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

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.

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.

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.

Given a directrix (line) and a focus (fixed point), what is the locus of points equidistant from the two?

  

080737a In the diagram below, town C lies on straight road p. Sketch the points that are 6 miles from town C. Then sketch the points that are 3 miles from road p. How many points satisfy both conditions?

6 mi6 mi 3 mi

3 mi

How many points are equidistant from two parallel lines and also equidistant from two points on one of the lines?(1) 1 (3) 3(2) 2 (4) 4

In the coordinate plane, what is the total number of points 5 units from the origin and equidistant from both the x- and y-axes?(1) 1 (3) 0(2) 2 (4) 4

Steve has a treasure map that shows two trees 8 feet apart and a straight fence connecting them. The map states that treasure is buried 3 feet from the fence and equidistant from the two trees.

a Sketch a diagram to show all the places where the treasure could be buried. Clearly indicate in your diagram where the treasure could be buried.b What is the distance between the treasure and one of the trees?

3 feet

3 feet

3 feet

4 feet

5 feet

Real life situations

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.

HW

locating an epicenter :You are given readings from 3 different seismographs:1) point A(-2, 2) and distance to the earthquake is 3 miles2) point B(4, -1) and distance to the earthquake is 6 miles3) 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)