       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,
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

True

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

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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