Fine the point on the line

Question

Find the point on the line 4x+3y–6=0 which is closest to the point (–4,1).

Answer 1

4x + 3y - 6 = 0

3y = -4x + 6

y = -4x/3 + 2

 

The closest point lies on the perpendicular.

 

y = 3x/4 + b

1 = 3(-4)/4 + b

1 = -3 + b

4 = b

y = 3x/4 + 4

 

Solve the system for the point.