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. > >
- References:
- vertices of a rectangle
- From: clarice <clariceane16@yahoo.com>
- vertices of a rectangle