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

```

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