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).
+128474 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)
