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#1 2012-11-09 22:52:00

danthemaths
Member
Registered: 2012-10-18
Posts: 2

Geometry Question - Please Help

I have a question saying "Hence find the coordinates of the point C such that AC is a diameter of this circle".

I already know:
Points: A(0,2) B(4,-2)
Equation of line AB: x^2+y^2-2x+2y=8   => and simplify that you get: (x-1)^2+(y+1)^2=10
Perpendicular Equation to line AB (through B): y=-x+2

I do not know how to work this out! Could you please explain to me step by step if u can on how to solve this?

Thanks in advance
Dan

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#2 2012-11-09 23:23:01

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,303

Re: Geometry Question - Please Help

hi Dan,

Welcome to the forum.

How much was given in this question?

Just points A and B is not enough to fix one circle, so I'll assume you were told the equation as well.

So (1,-1) is the centre of the circle.  Let's call it O.

Then from A to O is the same as from O to C.  (as you want AOC to be a straight line and diameter.)

That's enough to just count across and down from A to O and hence find C without needing perpendicular lines.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-11-09 23:33:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,453

Re: Geometry Question - Please Help

Hi danthemaths;

First you should always have a drawing to help you think about the question and also to pose it for others.

Perpendicular Equation to line AB (through B): y=-x+2

Although it does not matter I am not getting that equation for the perpendicular.

View Image: 2012-11-10_033225.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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