Equation of a line

Question

Fnd the equation of the line S y = f(x) whose closest point to point A (3,4) is point B (5,5). find the coordinates of the normal vector of the line S.

Answer 1

f(x) = -2x +15

vector from the origin to closest point on the line

<5,3>

it helps to graph the points and lines

normal means perpendicular with negative inverse for the line

if (5,5) is the closest point to (3,4) find the slope of a line through them =difference in y coordinates divided by difference in x coordinates = (5-4)/(5-3)= 1/2

then find the negative inverse =-2

y=-2x + b is the equation of the line through (5,5) that you want.

solve for b

5=-2(5)+b

b =5+10=15

y=-2x+15