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):
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.
