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Re: vertices of a rectangle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131277] Re: vertices of a rectangle
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Sun, 23 Jun 2013 22:56:18 -0400 (EDT)
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  • References: <20130623004628.C1BE569C1@smc.vnet.net>

pts = {a = {1, 4}, b = {7, 0},
   c = {5, -3}, d = {-1, 1}};


m = Mean[pts];


Graphics[
 {Text[#, ToExpression[#],
     1.5 Sign /@ (m - ToExpression[#])] & /@
   {"a", "b", "c", "d"},
  Blue, Polygon[pts],
  AbsolutePointSize[5],
  White, Point[m],
  Red, Point[pts]},
 Frame -> True, Axes -> False,
 PlotRange -> {{-1.5, 7.5}, {-4, 5}}]


To be a rectangle, each of the four corner angles must be Pi/2 radians


Union[
  VectorAngle @@@
   {{d - a, b - a}, {a - b, c - b},
    {d - c, b - c}, {c - d, a - d}}] ==
 {Pi/2} == {90 Degree}


True


Also, the opposite sides are of equal length


Norm[a - b] == Norm[c - d] == 2 Sqrt[13]


True


Norm[b - c] == Norm[a - d] == Sqrt[13]


True


The area is


area = Norm[a - b]*Norm[b - c]


26



Bob Hanlon


On Sat, Jun 22, 2013 at 8:46 PM, clarice <clariceane16 at yahoo.com> wrote:

> need help for this :))
>
> show that the points A=(1,4), B=(7,0), C=(5,-3), D=(-1,1) are the vertices
> of the rectangle, find it's area.
>
>


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