Question 200407
Determine the shortest distance from the origin to the line represented by y=1/2x-2.
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The shortest distance from a point to a line is along the line perpendicular.
The slope of y = (1/2)x - 2 is 1/2.
The line perpendicular has a slope that's the negative inverse, m = -2.
y-y1 = m(x-x1) is the eqn of the perpendicular line, where (x1,y1) is (0,0)
y = -2x
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Solve for x at the intersection:
-2x = x/2 - 2
-4x = x - 4
x = 0.8
y = -1.6
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The distance is sqrt(0.8^2 + 1.6^2)
= sqrt(3.2)
= 0.8*sqrt(5)
= ~1.7889