What is the distance from the origin to the point on the line #y=-2x+5# that is closest to the origin?

1 Answer
Dean R.
Apr 25, 2018

#sqrt{5}#

Explanation:

Our line is

#y = -2x + 5 #

We get the perpendiculars by swapping coefficients on #x# and #y#, negating one of them. We're interested in the perpendicular through the origin, which has no constant.

#2y = x #

These meet when #y = -2(2y) + 5 = -4y + 5# or #5y =5# or #y=1# so #x=2#. #(2.1)# is the closest point, #sqrt{2^2+1}=sqrt{5}# from the origin.

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