The coordinates of the foot of the perpendicular from the point 2,3 on the line −y+3x+4=0 are given by
37/10, −1/10
−1/10, 37/10
10, 37,−10
2/3,−1/3
h-x1a=k-y1b=-(ax1+by1+c)a2+b2
(x1,y1)=(2,3);ax+by+c=3x-y+4
Therefore, the foot is h=−1/10, k=37/10.