How do I get a point from two points using a right triangle?

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In the image the triangle is made up of 3 points, 2 of which are found, the third one is missing, not sure how to get this last point. [Need an Equation]

triangle missing a point

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Distance from $(x,y)$ to $(4,4)$ is $|\sqrt{(x-4)^2+(y-4)^2}| = 1$

Distance from $(x,y)$ to $(4,1)$ is $|\sqrt{(x-4)^2+(y-1)^2}| = |\sqrt{10}|$

Square both sides of both these equations and subtract one from the other to get $(y-1)^2-(y-4)^2=10-1=9$. So you get, $$y^2+1-2y-(y^2+16-8y)=9\Longrightarrow 6y-15=9\Longrightarrow y=4$$ If you put $y=4$ an any one of the first two equations you will get $x=5$.