Question

Find the point on the line −2x+6y+4=0 which is closest to the point (1,−3)

Answer 1

Answer: (1/5,-3/5)

Explanation:

`line:\quad -2x+6y+4=0\quad,\quad y=(1)/(3)x-(2)/(3)\\normal:\quad y+3=-3(x-1)\quad,\quad y=-3x\\intersection:\quad(1)/(3)x-(2)/(3)=-3x\quad,\quad x=(1)/(5),y=-(3)/(5)`