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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: 6,382

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: 86,436

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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