Can someone please help with this question Find the closest point on the line y=2x to (1,0)

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Can someone please help with this question Find the closest point on the line y=2x to (1,0)

Mathematics
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the closest point between two spots is a straight line that is perpendicular to it. right?
yes
then lets make a line perpendicular to this one the crosses thru the point (1,0)

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then where those lines meet is the nearest point right?
y = 2x; y = (-1/2)x is perpendicular to it.
0 = (-1/2)(1) + b 0 = -1/2 + 1/2 our equation is going to be y = (-1/2)x + 1/2
now where do these two equations meet up? y = 2x y = (-1/2)x + 1/2 2x = (-1/2)x + 1/2 2x + (1/2)x = 1/2 (5/2)x = 1/2 ---- --- 5/2 5/2 x = 1/5 the nearest point is: (1/5 , 2,5)
(1/5 , 2/5) if I can type today :)
y = (-1/2)(1/5) + 1/2 y = -1/10 + 5/10 y = 4/10 = 2/5 that chacks out good :)
you agree?
yes I do
good :) but I hope you do so because its right, and not becasue I said so ;)
Thanks

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