Find the point on the line − 2 x + 5 y + 1 = 0 which is closest to the point ( 4 , − 4 ) .

Answer 1

The closest point on the line shall be on the perpendicular to the line that passes through the given point.

Determine the slope of the given line.

Make the negative reciprocal of that slope

Use negative reciprocal of the slope and the point to determine equation of perpendicular.

Determine intersection of the given line and the line perpendicular