Find the point on the line -6x+5y-1=0 which is closest to the point (-3,1)
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 m1.
Step 2: Find the negative reciprocal of that slope; call this slope m2.
This is the slope of the line that is perpendicular to the original line.
Step 3: Use the point-slope form ( m2 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.