SOLUTION: Problem states: "Let P=(x,y) be a point on the graph of y= square root of x. Express the distance "d" from point P to the point (1,0) as a function of x." I get to "square root of

Algebra ->  Rational-functions -> SOLUTION: Problem states: "Let P=(x,y) be a point on the graph of y= square root of x. Express the distance "d" from point P to the point (1,0) as a function of x." I get to "square root of      Log On


   

Question 29436: Problem states: "Let P=(x,y) be a point on the graph of y= square root of x. Express the distance "d" from point P to the point (1,0) as a function of x."
I get to "square root of (x-1)^ + y^", then I'm confused. Please help
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
you are along the right lines but you have missed one crucial "leap of insight".

at any point on the curve, the x-value is x but the y-value is not just y...it is sqrt%28x%29.

So, the distance between A(1,0) and P(x,sqrt%28x%29) is:

+AP+=+sqrt%28%28x-1%29%5E2+%2B+%28sqrt%28x%29-0%29%5E2%29+
+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+%28sqrt%28x%29%29%5E2%29+
+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+x+%29+
+AP+=+sqrt%28%28x%5E2-x%2B1%29+%29+

this is the answer.

CHECK:
If P(0,0), the length of AP should be 1.
--> put x=0 into the formula and we get 1.

Pick say P(25,5), then from coordinate geometry, AP = sqrt%28601%29. Putting x=25 into the formula gives us this.

jon.