Find the point on the line which is closest to the point . ( , )

Question

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

(    ,    )

Answer 1

The first line (1) is y=-5/6 x -1.

The second line (2) y=ax+b has to be perpendicular, so:

a=6/5 Point (1,5) belongs to (2), so b=19/5

From (1) and (2) their intersection is the point P (-144/61 , 56/61)

Answer 2