Find the point on the line − 3 x + 7 y − 4 = 0 which is closest to the point ( − 1 , 1)

Question

Find the point on the line −3x+7y−4=0-3x+7y-4=0 which is closest to the point (−1,1)

your answer:

(. , )

Answer 1

y=3x/7+4/7

I can prove with similar triangles

d=distance

d=|y₀-mx₀-b|/√(1+m²)

where the point is (x₀,y₀), and m the line slope and b the y axis intercept

so

d=|1+3/7-4/7|/√(1+9/49)=6/√58

yikes, you need exact point

y=3x/7+4/7 is line

and

perpendicular line through x=-1,y=1

is

y=-7x/3-4/7

solving for x with y=y

58x/21=-40/21, x= -40/58

is the intersection x coordinate, plug into either equation for y