SOLUTION: Analytic geometry 11) Determine the shortest distance from the origin to the line represented by y=1/2x-2. (PLEASE) Thank you very much

Question 178074: Analytic geometry
11) Determine the shortest distance from the origin to the line represented by y=1/2x-2. (PLEASE)
Thank you very much
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine the shortest distance from the origin to the line represented by y=1/2x-2.
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Slope of the given line is (1/2).
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Slope of any line perpendicular to the given line is -2
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Equation of a line with slope -2 and passing thru (0,0)
is y = -2x
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Intersection of the two lines = ?
-2x = (1/2)x-2
(5/2)x = 2
x = 4/5
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y = -2(4/5) = -8/5
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Pt. of intersection is (4/5, - 8/5)
============================
Distance from origin to the point of intersection is ?
d = sqrt[(4/5)^2 + (-8/5)^2]
d = sqrt[(16 + 64)/25] = sqrt[80/25]
d = (4/5)sqrt(5)
========================
Cheers,
Stan H.
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