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

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Presentation transcript:

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

Mathematicians sometimes find it convenient to describe a figure as a locus. (Locus is a Latin word meaning “place” or “position.”) Definition – A locus is a set consisting of all the points, and only the points, that satisfy specific conditions. The plural form is loci. We will assume all points are coplanar unless otherwise stated.

What is created when we put all the points together? Easy example Find the locus of all points 3 units from a point. 3 A circle! I always knew I was the center of the universe!

4 step Procedure for Locus Problems 1.Find a single point that satisfies the given condition(s). 2.Find a second such point, and a third, and so on, until you can identify a pattern. 3.Look outside the pattern for points you may have overlooked. Look within the pattern to exclude points that do not meet the conditions. 4.Present the answer by drawing a diagram and writing a description of the locus.

Example 2 What is the locus of all points equidistant from the sides of an angle? The locus of all points equidistant from the sides of an angle is the angle bisector of the angle.

Example 3 What is the locus of points 3 cm from a given line? The locus of all points 3 cm from a given line is 2 lines parallel to the given line, 3 cm on either side of it.

More Examples: What is the locus of points 2 in from a given circle whose radius is 5 in? Find the locus of points less than 3 cm from a given point A.

Last example Write the equation of the locus of points equidistant from points A(1, 4) and B(7, 8)

Summarize your notes What do you personally need to remember when you are trying to find the locus of points? HW: WS 14.1