Find the point on the line -6x+5y-1=0 which is closest to the point (-3,1)

mharrigan920 Jun 16, 2020

#1**+1 **

The shortest distance from a point to a line is the perpendicular distance from that point to that line.

Step 1: Find the slope of the line -6x + 5y - 1 = 0. Call this slope m_{1}.

Step 2: Find the negative reciprocal of that slope; call this slope m_{2}.

This is the slope of the line that is perpendicular to the original line.

Step 3: Use the point-slope form ( m_{2} and the point (-3,1) ) to find the equation of the line through

the point (-3,1) that is perpendicular to the original line.

Step 4: Using the original equation and the equation that you found in step 3, find the point of

intersection of these two lines. This is the answer.

geno3141 Jun 16, 2020