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/
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