Math Is Fun Forum

jussipe

Member

Registered: 2008-10-31

Posts: 2

Find the Co-ordinates!!

Find the Co-Ordinates of all points P on the X-axis so that  the line through A(1, 2 and P is perpendicular to the line through B(8, 3) and P.

please make it quick!!!

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: Find the Co-ordinates!!

let the coordinates of the point P is (x,y)
Now we can consider the points A(1,2) and B(8,3) as the points of end points of diameter of the circle which passes through A, B and P
Now the equation of the circle is (x-1)(x-2)+(y-8)(y-3)=0

Since the Point lies in the x axis, y=0
Now the above equation becomes (x-1)(x-2)+24=0
which is quadratic equation now solve the equation we get the required answer.

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Find the Co-ordinates!!

http://www.mathisfunforum.com/viewtopic.php?id=10891

I solved this problem in the above link using vectors and basic algebra.

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: Find the Co-ordinates!!

alternative method
Let P(x,0) be the point in x-axis
Now slope of PA is (2-0)/(1-x) and the slope of the line PB is (3-0)/(8-x)
Since PA and PB are perpendicular
product of two slopes is -1 hence
{(2-0)/(1-x)}*{(3-0)/(8-x)}=-1
which on simplifying
6=-8+9x-x^2
x^2-9x+14=0
Or, (x-2)(x-7)=0
or x=2,7
Hence the required points are (2,0) and (7,0)

Last edited by gyanshrestha (2008-11-03 01:17:19)

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WiZaRd

Real Member

Registered: 2006-09-22

Posts: 570

Re: Find the Co-ordinates!!

Thank you very much!! gyanshrestha!!

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Be Happy!

jussipe

Member

Registered: 2008-10-31

Posts: 2

Re: Find the Co-ordinates!!

thank you very much. i owe you x,..,0