### 12.18.3 The trace of a geometric object: trace

The trace command takes as argument a geometric object which depends on a parameter.
trace draws the trace of the object as the parameter is changed or the object is moved in Pointer mode.

For example, to find the locus of points equidistant from a line D and a point F, we can create a point H on the line D. Since the point To do this, open a graphic window (Alt-G) and type in the following commands, one per line.
First, create a line D (using sample points) and a sample point F.
Input

A := point(-3-i)
B := point(1/2 + 2*i)
D := line(A,B,color=0)
F := point(4/3,1/2,color=0)

The create a point H on the line D which we can move around.
Input:

assume(a=[0.7,-5,5,0.1])
H := element(D,a)

To find a point equidistant from D and F, find the point M where the perpendicular to D (at H) intersects the perpendicular bisector to HF, and trace that point.
Input:

T := perpendicular(H,D)
M := single_inter(perpen_bisector(H,F),T))
trace(M)

Then as the point H on the line moves (by changing the value of a with the slider), we will get the trace of M.

To erase traces, add traces, activate or deactivate them, use the Trace menu of the M button located on the right side of the geometry screen.