SOLUTION: Analytic Geometry 11. Determine the shortest distance from the origin to the line represented by y=1/2x-2. Thank you!@@

Question 199380: Analytic Geometry
11. Determine the shortest distance from the origin to the line represented by
y=1/2x-2.
Thank you!@@
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The given line is already in slope-intercept form, so you can determine the slope by inspection. Determine the slope of a line perpendicular to the given line by calculating the negative reciprocal of the slope of the given line.

Use the point-slope form of the equation of a line to determine the equation of a line perpendicular to the given line that passes through the origin.

Where

is the negative reciprocal of the slope of the given line and

is the origin, (0,0).

The given line and its perpendicular through the origin form a system of equations. Solve the system for the point of intersection.

Finally use the distance formula:

Where

and

are the point of intersection and the origin to calculate the distance from the origin to the given line.

John

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