Diameter Endpoint

Date: 01/26/2003 at 18:44:15
From: Brian
Subject: Linear Equations

The center of a circle is (-4,7) and one endpoint of a diameter is 
(2,-1). What is the other endpoint of the diameter?

It's easy to find the answer when you graph it, but how would you 
find the other point without using the graphing method. Is there any 
formula you follow?

Thank you so much for your time.

Date: 01/27/2003 at 12:04:14
From: Doctor Roy
Subject: Re: Linear Equations

Hi,

Thanks for writing to Dr. Math.

Remember that the diameter is twice the radius. Since one endpoint is
given, and you know the center, you also know that the other endpoint
is the same distance from the center.

To get to the center from the endpoint, we subtract 6 from the
x-coordinate and add 8 to the y-coordinate. 

   -4 -2 = -6 and 7 - (-1) = 8

So, in order to get the other endpoint from the center, we should
subtract 6 from the x-coordinate of the center and add 8 to the
y-coordinate of the center.

If you examine your answer, you will find that -4 - 6 = -10 and 
7 + 8 = 15, which is the answer you got.

Does that help?  Please feel free to write back with any questions you
may have.

- Doctor Roy, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/27/2003 at 18:24:31
From: Brian
Subject: Thank you (Linear Equations)

Thanks so much Dr. Roy, it was a real help to me.