Greek for Geo: March 5: How do we find the locus of points? (AIM)

Aim: How do we find the locus of points?

When finding the locus or the locus of points, you should go by this definition:

- the set of all points that satisfy a given condition.

The locus is usually graphed on a general graph of a given equation. but this is only sometimes, depending on the question (what is asked).

A single point:

When graphing the locus of points that are equidistant from a single point, it'll create a circle with the original point at it's center point. Also with the set of points in the line of the circle !

2 points:

When graphing the locus of points that are equidistant from 2 points , it'll be the perpendicular bisector of the line segment connecting the 2 points. This forms a line through the middle of the 2 points.

The 2 points which are P & Q
have a line that makes a perpendicular
bisector through the line that P & Q.

A line:

When graphing the locus of points that are equidistant from a line are 2 lines (that are on opposite sides), it'll be the same distance [equidistant] and parallel to the line. This leaves 2 parallel lines on opposite sides of the original line.

2 lines:

When graphing the locus of points that are equidistant from 2 parallel lines is another line (half-way between both lines), then each of the them will be parallel. So it'll be a line through the middle of the 2 lines.

These locus of points are equidistant
from the y-axis. They are on the
lines x=-1.5 and x=1.5.

2 intersecting lines:

When graphing the locus of points that are equidistant from 2 intersecting lines, it'll bisect the angles formed by the original lines. That means that the 2 intersecting lines are half-way between the 2 original lines.

Line 1 and Line 2 intersect at the origin.

Sources Cited:

Greek for Geo