Aim: How do we find compound locus?

March 7,2012 Aim: How do we find compound locus?

Answer:
Compound Locus: a compound locus is when their are two or more compound problems expressed in one mathematical problem or at the same time
Great steps to help with solving compound locus's 

Strategy for Solving Compound Locus Problems

If TWO locus conditions exist in a problem (a compound locus), prepare each condition separately ON THE SAME DIAGRAM.  After the two conditions are drawn separately, count the number of points where the two loci conditions intersect.   (It may help to draw the locus locations as dotted lines.   Then find where the dotted lines cross.) Steps: 1.  Draw a diagram showing the given information in the problem.   2.  Read carefully to determine one of the needed conditions.  (Look for the possibility of the words "AND" or "AND ALSO" separating the conditions.) 3.  Plot the first locus condition.  If you do not see one of the locus theorems at work in the problem, locate one point that satisfies the needed condition and plot it on your diagram.  Then locate several additional points that satisfy the condition and plot them as well.  Plot enough points so that a pattern (a shape) is starting to appear, or until you remember the needed locus theorem for the problem.  4.  Through these plotted points draw a dotted line to indicate the locus (or path) of the points. 5.  Repeat steps 2-4 for the second locus condition. 6.  Where the dotted lines intersect will be the points which satisfy both conditions.  Thesepoints of intersection will be the answer to the compound locus problem.

An example of a Compound locus problem is: 

.

Parallel lines r and s are 8 meters apart, and A is a point on line s.  How many points are equidistant from r and s and also 4 meters from A?  (The green highlighted is the first  locus condition, and the orange highlighted is the second locus.) Answer:    The answer will be 1 point, where the circle is tangent to the line.  Notice where the two loci intersect, marked with "X".  The red line is first locus condition and the blue circle is the second locus condition.

Choose:  0  1 2 3

Try it yourself:

1.

What is the number of points in a plane two units from a given line and three units from a given point on the line?

Choose:  1  2   3 4

Answer:

The answer will be 4 points.  Notice where the two loci intersect, marked with "X".  The red lines are the first locus condition and the blue circle is the second locus condition.



Works Cited:

http://regentsprep.org/regents/math/geometry/GL3/PracLocC.htm#
http://regentsprep.org/regents/math/geometry/GL3/LocusCom.htm