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A point (x,y) is a distance of 12 units from the x-axis. It is a distance of 10 units from the point (1,6). It is a distance n from the origin. Given that x>1, what is n?

 Feb 4, 2022
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The y-coordinate must be \(12\), because that is the only way to be \(12\) units from the x-axis.

 

I think of distance as a right triangle, with the distance between the \(2\) points being the hypotenuse.

 

We know that the height of the triangle is \(6\), and because the hypotenuse(distance) is \(10\), its x-axis is 8 units away from \(8\).

 

 This means that the coordinates are \((9,12)\). It can't be \((-7,12)\), because \(x\) is not greater than \(1\)

 

This means that \(\color{brown}\boxed{n=15}\)

 Feb 4, 2022

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