This applet demonstrates the basics of creating a locus equation object in GeoGebra.
[list=1] [*]In Step 1 line AB (denoted by "a") is defined. [*]In Step 2 its equation is also displayed (numerically). [*]Now we define point C and mirror the line to the point (Step 3). How? In Step 4 we put point D on line a and mirror it on C (Step 5) to get point D'. [*]Now the locus of point D' while point D is moving on line a, is the mirror image of line a, i.e. the mirrored line a' (Step 6). [*]Finally in Step 7 we obtain the equation of line a'. [/list] Some actions to try out: [list=1] [*]Drag point D and check that D' is its mirror image to point C. [*]Drag point C and try to search for such a place for it to make the coefficients of equation a' to be "larger" numbers. Note that these coefficients are always integers. [*]Drag points A and B as well. Note that the equation of line a may contain numeric values, i.e. it is computed numerically. [/list] Dragging may be slow under some systems and conditions. Turn on the next page to learn how to speed up animation in such cases.