SOLUTION: 3. Find the shortest distance from the point P(-5, 9) to the line 3x-2y=6. Round to the nearest tenth if necessary. Thank you very much!!!!!

Question 189849: 3. Find the shortest distance from the point P(-5, 9) to the line 3x-2y=6. Round to the nearest tenth if necessary.
Thank you very much!!!!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First take the given equation and put it into slope-intercept form, then determine the slope by examining the coefficient on x.

Next use:

To calculate the slope of a line perpendicular to the given line.

Using the given point and the slope of the perpendicular you just calculated in the point-slope form of the equation of a line,

, derive the equation of the perpendicular to the given line that passes through the given point.

The original equation and the just-derived equation for the perpendicular form a system of equations. Solve this system for the point of intersection of the the two lines using any appropriate method. Since you already have the given equation in slope-intercept form, the substitution method may be the easiest.

Determine the distance between the given point and the just-derived point of intersection using the Distance Formula:

The result of this final calculation is the answer to the problem.

John

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