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Determine the coordinates of the point P on the line y=-x+6 such that P is equidistant from the points A(10,-10) and O(0,0) (that is, so that PA=PO). Express your answer as an ordered pair (a,b).

 Mar 12, 2019
 #1
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Answer is (8,-2)

 Mar 12, 2019
 #2
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Let P =  ( x, -x + 6) = (x, 6 - x)

 

We want to solve this

 

( Distance from P to (0,0) )^2  = (Distance from P to (10, -10) )^2

 

x^2 + (6 - x)^2  =  [ ( x - 10)^2 + ( 6 - x + 10)^2

 

x^2 + x^2 - 12x + 36  =   x^2 - 20x + 100  + x^2 - 32x + 256     simplify

 

-12x + 36  =  -52x + 356

 

40x =  320

 

x = 8

 

And 

 

y = -(8) + 6  =  -2

 

So...P  =  ( 8, -2)

 

 

cool cool cool

 Mar 12, 2019

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