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# Analytical Geometry

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this is based on Analytical Geometry, all the questions which I am asking. I am just curious on how to solve these problems

Oct 11, 2018

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$$\text{A point on the line }y=-x+6 \text{ is given by }(x, -x+6)\\ \text{the squared distance between two points u and v is given by}\\ d^2(u,v)=(u_x-v_x)^2+(u_y-v_y)^2 \\ \text{if the distance between two points is equal so will the squared distance be, so}\\ d^2[(10,-10),(x,-x+6)] = d^2[(0,0),(x,-x+6)] \\ (10-x)^2 + (-16+x)^2 = x^2 + (-x+6)^2 \\ 2 x^2-52 x+356=2x^2-12 x+36 \\ 320=40x\\ x=8,~y=(-x+6) = -2\\ (x,y) = (8,-2)$$

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Oct 11, 2018
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Thank you rom

Oct 11, 2018