SOLUTION: Determine the shortest distance from the point D(5,4) to the line represented by 3x+5y-4=0

Question 804862: Determine the shortest distance from the point D(5,4) to the line represented by 3x+5y-4=0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The shortest distance from a point to a line is the distance between the given point and the point of intersection of the line perpendicular to the given line and passing through the given point.

Step 1: Determine the slope of the line represented by the given equation (hereinafter referred to as the given line).

Step 2: Calculate the slope of a perpendicular to the given line by taking the negative reciprocal of the slope of the given line.

Step 3: Use the point-slope form, the coordinates of point D, and the slope calculated in step 2 to derive an equation of the line perpendicular to the given line that passes through point D.

where

are the coordinates of the given point and

is the calculated slope.

Step 4: Solve the 2X2 linear system consisting of the given equation and the equation derived in step 3.

Step 5: Use the distance formula to calculate the distance between point D and the point of intersection represented by the coordinates of the ordered pair that is the solution set from step 4.

where

and

are the coordinates of the given (or derived) points.

John

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