Distance to the Corner of a Rectangle

Date: 05/01/2001 at 21:45:03
From: Jay 
Subject: Geometry

A point P is located in the interior of a rectangle so that the 
distance from P to one corner is 3 units, from P to the opposite 
corner is 5 units, and from P to a third corner is 4 units. Find the 
distance from P to the fourth corner. Explain and justify your answer.

Date: 05/02/2001 at 05:09:04
From: Doctor Floor
Subject: Re: Geometry

Hi, Jay,

Thanks for your question.

Here is a figure that shows your question:

   

We are looking for the value of x.

We can apply the Pythagorean theorem a couple of times:

     a1^2 + b1^2 =  9
     a1^2 + b2^2 = 16
     a2^2 + b2^2 = 25
     a2^2 + b1^2 = x^2

If we subtract the second equations from the first, we get:

     b1^2 - b2^2 = -7

and if we add that to the third equation, that yields:

     a2^2 + b1^2 = 18

Together with the fourth equation, this shows that:

     x^2 = 18
       x = sqrt(18)

If you need more help, just write back.

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/