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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- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-outx@smc.vnet.net
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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