       Re: vertices of a rectangle

• To: mathgroup at smc.vnet.net
• Subject: [mg131276] Re: vertices of a rectangle
• From: Tomas Garza <tgarza10 at msn.com>
• Date: Sun, 23 Jun 2013 22:55:58 -0400 (EDT)
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• References: <20130623004628.C1BE569C1@smc.vnet.net>

Uppercase letters are reserved for Mathematica's own symbols. So, if your four points are
In:= {a = {1, 4}, b = {7, 0}, c = {5, -3}, d = {-1, 1}}

Out= {{1, 4}, {7, 0}, {5, -3}, {-1, 1}}
Show, first, that the vectors a-d and b-c are parallel:

In:= VectorAngle[a - d, b - c]

Out= 0

and so are the vectors b-a and c-d:

In:= VectorAngle[b - a, c - d]

Out= 0

Any two adjoining sides are orthogonal:
In:= VectorAngle[a - d, b - a]

Out= Pi/2

Check that the parallel sides have the same length, so the four points determine a rectangle.
In:= EuclideanDistance[d, a] == EuclideanDistance[c, b]

Out= True

In:= EuclideanDistance[b, a] == EuclideanDistance[c, d]

Out= True
Determine the length of the sides

In:= d1 = EuclideanDistance[d, a]

Out= Sqrt

In:= d2 = EuclideanDistance[b, a]

Out= 2 Sqrt

The area of the rectangle is

In:= d1 d2

Out= 26

-Tomas

> From: clariceane16 at yahoo.com
> Subject: vertices of a rectangle
> To: mathgroup at smc.vnet.net
> Date: Sat, 22 Jun 2013 20:46:28 -0400
>
> 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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