Re: find area bounded by three linear functions
- To: mathgroup at smc.vnet.net
- Subject: [mg68375] Re: find area bounded by three linear functions
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 3 Aug 2006 06:06:36 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <eaprqf$s4d$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
T Harris wrote:
> How can I get Mathematica to find the area of the region bounded by all
> three of the following linear functions? I have tried searching and can't
> find it. What do I search for to find the commands to accomplish this? I
> calculated by hand and come up with about 3.1623 sq. units for area above
> the x-axis and 8.8378 sq. units below it. The total area for the scalene
> triangle formed is 12 square units by my calculations using Heron's formula.
>
> X=3Y; X+Y=0; 7X + 3Y =24
>
> Thanks,
>
> T Harris
>
Half of the Eucledian-norm of the vector cross product yields the area
of the triangle defined by the points of intersection of the three lines.
eqns = {x == 3*y, x + y == 0, 7*x + 3*y == 24}
pts = ({x, y} /. Flatten[Solve[#1, {x, y}]] & ) /@ Subsets[eqns, {2}] /.
{x_, y_} -> {x, y, 0}
Norm[Cross[pts[[2]] - pts[[1]], pts[[3]] - pts[[1]]]]/2
returns 12.
HTH,
Jean-Marc