Perpendicular Bisector Theorem

Author

Eric W. Weisstein
July 22, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/PerpendicularBisectorTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PerpendicularBisectorTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Graphics`Colors`;
<<GIF`;

Figure

t=Table[
{Line[{{-1,0},{0,h},{1,0}}],
Line[{{0,.5},{0,h}}]},
{h,-.5,.5,.2}];

Length[t]

Show[GraphicsArray[Partition[Graphics[{{PointSize[.04],Thickness[.01],
{Red,Line[{{-1,0},{1,0}}],Point/@{{-1,0},{1,0}}},
{Blue,Line[{{0,-.5},{0,.5}}],Point/@{{0,-.5},{0,.5}}}
},#},PlotRange->1.1{{-1,1},{-1,1}}]&/@Reverse@NestList[Rest,t,Length[t]],3]
]]

t=Table[
{Line[{{-1,0},{0,h},{1,0}}],
Line[{{0,.5},{0,h}}]},
{h,-.5,.5,.1}];

Export[gifs<>"perpbist.gif",Show[Graphics[{{PointSize[.02],Thickness[.01],
{Red,Line[{{-1,0},{1,0}}],Point/@{{-1,0},{1,0}}},
{Blue,Line[{{0,-.5},{0,.5}}],Point/@{{0,-.5},{0,.5}}}
},#}],PlotRange->1.1{{-1,1},{-1,1}}]&/@Reverse@NestList[Rest,t,Length[t]]
]//Timing