SOLUTION: Find two points on the x-axis that are 10 units from point (1,8).

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Question 983030: Find two points on the x-axis that are 10 units from point (1,8).
Found 3 solutions by josgarithmetic, solver91311, macston:
Answer by josgarithmetic(39620) About Me  (Show Source):
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That means y=0.
You want some points (x,0), two different x.

Distance formula with the coordinate values substituted,sqrt%28%28x-1%29%5E2%2B%280-8%29%5E2%29=10

%28x-1%29%5E2%2B%2864%29=100

x%5E2-2x%2B1%2B64-100=0

x%5E2-2x-35=0

%28x-7%29%28x%2B5%29=0
x=7 or x=5.

Answer by solver91311(24713) About Me  (Show Source):
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If the two points are on the -axis, then they must have coordinates and . Further, the following must be true:



This will reduce to a quadratic and the two roots will be the missing -coordinates.

John

My calculator said it, I believe it, that settles it

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
This forms two right triangles with height (b)=8 and hypotenuses (c)=10.
The other legs will be the distance (a) on the x axis from point (1,0)
a%5E2%2Bb%5E2=c%5E2
a=sqrt%28c%5E2-b%5E2%29
a=sqrt%2810%5E2-8%5E2%29
a=sqrt%2836%29
a=plus or minus 6
So the two points are (1+6,0) and (1-6,0) or (7,0) and (-5,0)