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What is the x- coordinate of the point on the x-axis that is equidistant from points A( -2, 0) and B(0,\(8\))?

 Apr 25, 2022
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Using the distance formula, we have the following system, where:

 \(x = \) x co-ordinate of the point

\(y = \) distance between 2 points

 

\(64+x^2=y^2\)  Distance between \((0,8)\) and \((x, 0)\)

\(y=x+2\)        Distance between \((-2,0)\) and \((x,0)\)

 

Substituting in the second equation, we have: \(64+x^2=x^2+4x+4\)

 

Solving for x, we find \(\color{brown}\boxed{x = 15}\)

 Apr 25, 2022

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