Question: How do we find the locus of points?

Answer: So what is a locus? Well a locus is the set of all points that satisfy a given condition.

The plural of locus is loci

Ok now, let me explain how to identify the different types of locus problems.

There are 5 types of locus problems.

LOCUS PROBLEM #1: Finding the locus of one point

Figure 1

Whenever you are trying to find the locus of one point, the loci will be equidistantly away from the point. In figure 1, for example, the locus of points away from point P will be an equal distance away from the point, thus it will produce a circle with the original point (P) in the center.

LOCUS PROBLEM #2: Finding the locus of two points

Figure 2

Whenever you are trying to find the locus of two points, the loci will be a line through the middle of the two points. As illustrated in figure 2, for example, the locus of points away from points P and Q will be the perpendicular bisector of the line segment connecting the two points.

LOCUS PROBLEMS #3: Finding the locus of a line

Figure 3

Whenever you are trying to find the locus of a line, the loci will be two parallel lines on opposite sides of te original line. As illustrated in figure 3, for example, the locus of points of line L will be two lines, opposite sides, equidistant and parallel to the original line.

LOCUS PROBLEM #4: Finding the locus of two lines

Figure 4

Whenever you are trying to find the locus of two lines, the loci will be a line through the middle of the two lines. As illustrated in figure 4, for example, the locus of points of lines L1 and L2 will be another line halfway between both lines, and parallel to each other.

LOCUS PROBLEM #5: Finding the locus of two intersecting lines

Figure 5

Whenever you are trying to find the locus of two intersecting lines, the loci will be two intersecting lines halfway between the two original lines. As illustrated in figure 5, for example, the locus of points of lines L1 and L2 will be two additional lines that bisect the angles formed by the original lines.

NOW YOU TRY! :D

What shape would the locus of points 3 inches away from point A form?

1.A circle

2.A square

3.A triangle 

4.A rhombus