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What is the x-coordinate of the point on the x-axis that is equidistant from points A(-2,4) and B(0,18)?

 May 15, 2022
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Let the distance be \(d\), and let the x-coordinate of the point be \(a\)

 

Using the distance formula, we can derive the following two equations: \(d^2 =a^2 + 18^2\) and \(d^2 = 4^2 + (a+2)^2\)

 

Setting the 2 equations equal to each other gives \(a^2 + 18^2 = 4^2 + (a+2)^2\)

 

Simplifying the right-hand side gives us: \(a^2 + 18^2 = 4^2 + a^2 + 4a + 4\)

 

Now, we have to solve for a, which is our final answer. 

 

Can you take it from here?

 May 15, 2022

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