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[1]:= {a = {1, 4}, b = {7, 0}, c = {5, -3}, d = {-1, 1}}

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

In[2]:= VectorAngle[a - d, b - c]

Out[2]= 0

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

In[3]:= VectorAngle[b - a, c - d]

Out[3]= 0

Any two adjoining sides are orthogonal:
In[4]:= VectorAngle[a - d, b - a]

Out[4]= Pi/2

Check that the parallel sides have the same length, so the four points determine a rectangle.
In[5]:= EuclideanDistance[d, a] == EuclideanDistance[c, b]

Out[5]= True

In[6]:= EuclideanDistance[b, a] == EuclideanDistance[c, d]

Out[6]= True
Determine the length of the sides

In[7]:= d1 = EuclideanDistance[d, a]

Out[7]= Sqrt[13]

In[8]:= d2 = EuclideanDistance[b, a]

Out[8]= 2 Sqrt[13]

The area of the rectangle is

In[9]:= d1 d2

Out[9]= 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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